Best order to get into the show without having to watch everything?

Strange New Worlds has been a hit, and for good reason. I'd say that's a worthy starting point. Lower Decks is really fun and full of references that might entice you to revisit earlier series (but really shouldn't hinder your enjoyment.
I tend to think new viewers should just start with whatever's present, meaning the "new" stuff. Of course there are some older series that are also good starting places (if you are primed for their more episodic nature, something younger viewers may not be familiar with).
- SNW second season hasn't been as good as the first so far
  
  Gasp. Even with a courtroom episode whose outcome could alter the Federation as we know it?
  Edit: lol, timely posting of a relevant meme in the Risa community: https://discuss.tchncs.de/post/334726

TNG is, imo, the gold standard and an excellent starting point if you’re not looking to jump straight into Strange New Worlds. Its episodes are generally pretty self-contained, so you won’t be punished terribly for jumping around if you’re just looking to get a taste, and will still be able to enjoy the great episodes it has to offer, but you will get more context the more episodes you’re willing to watch.
Plenty of folks have compiled lists of which episodes are skippable vs worth watching, and there’s pretty universal agreement on which are iconic must-watch episodes, so there’s nothing wrong with following one of those for a first watch. Here’s an example. I’d recommend using the list at the bottom of that page (or another rated list) as a guide, and experiment a bit to figure out a good baseline for how low of a rating is acceptable and how many episodes you can tolerate in your first watch through.
Note that season 1 is widely regarded as the weakest, where the show is trying to emulate ToS and hasn’t yet come into its own, and you can skip episodes more liberally here, or even come back to it later.
- Agreed! I think it comes at the cost of character development to some extent, since if you watch straight through, it feels like some of the characters just "reset" after enduring enormous, life-changing events, but it really is constructed in a way that makes it watchable from any point (except maybe the 2-parters.) New series have very much moved away from that style.
  I'm always tempted to tell people to skip the first season and revisit it later as well, but I guess it introduces some interesting things that the series periodically circles back to, so who knows. I watched it after many random episodes, so I still think of it as a sort of wonky prequel.
- If you want to watch more ToS, you can similarly cherry-pick your watch list there, as there are some stand-out episodes. I’d definitely recommend at least watching The Menagerie for context before SNW (or Captain Pike’s appearance in Discovery).
  DS9 is some of the very best of Trek, but you’re going to want to actually watch it through; it’s got much larger story arcs and character development than ToS, TNG, and Voyager. It takes a couple of seasons to really pick up, but is well worth it. If you’re not ready to sit through that many subsequent episodes yet, you can wait until you have a better feel for the series. But don’t sleep on this one, it’s fantastic.
  Those are my highlights for earlier Trek, but you can’t really go wrong as long as you’re enjoying what you’re watching!

Watch guides for every show. https://www.letswatchstartrek.com/
- Ooh! That is a really neat guide. I'm a seasoned trekkie and am still going to find this very useful.
- That's how I got started. Followed their guides through TNG, DS9, and VOY and was not disappointed

If you’re just getting into Trek, start with TNG season 3. Follow that up either with TNG seasons 1 & 2, or jump into Voyager.
For a darker Trek, watch DS9 - but be aware the first few seasons are very uneven and it gets a LOT better. It’s arguably the best of all the Trek series and well worth the investment to get past the first few seasons.
Enterprise was ok. It’s held up well, except for the theme song which was always trash. Don’t watch the series finale - just, don’t.
For the new series, SNW is the best of the live action bunch. Picard S1 and S2 are steaming piles while S3 was enjoyable and what S1 should have been. I personally enjoyed S1 and S2 of Discovery, while everything past that was truly terrible IMO. Prodigy was really good, if you can get past that it’s geared towards kids (which is obvious from time to time).
You’ve already enjoyed Lower Decks, so 👍
- Don’t watch the series finale - just, don’t.
  But why? Terra Prime was a perfectly fine final for the series.
  
  💯
- The enterprise opening theme rules and you cant convince me otherwise.

TNG season 3 onward.
Movie First Contact.
DS9. Skip around if you want. Look at the ratings. There's a lot of seasons and you don't need every episode
Voyager. The first 1 or 2 seasons were weak, then it's ok. You can watch based on ratings I think.
You can skip TOS. It has its own campiness. Watch if you want to understand Trek at its most uh Roddenberry.
Somewhere along the way:
Movie Wrath of Khan, just for the history.
Movie The Voyage Home. Just a fun feel good movie.
- I'm gonna throw Star Trek V in there under the label of "so bad it's kind of good".
  
  I will die on the hill that V is not a bad film. It has some cringe parts, sure, and the budget situation was obviously bad. There is some good stuff in there though.
  Sybok is actually one of my favorite characters in all of Trek, and brilliantly acted. I feel your pain. Share it with me.
  ::: spoiler The whole plot of a charlatan leading people to a promised land only to discover his own hubris -- and then try to vindicate himself -- is really quite good. :::

Can't really go wrong if you start TNG at season 3.

If you want the most “universally enjoyed” I’d say start with TNG season 2. Then once you’re finished maybe check out DS9

I think most people agree that TNG is either at the top, or close to the top for best series. There's also a smaller, diehard group that think DS9 is the best trek (myself included).
TNG is more adventurous where the crew is always on the side of morality and reason, and use wits and principles to overcome obstacles. Every episode is an adventure, and each adventure varies greatly from saving a planet from destruction or saving someone from their own mind. DS9 has larger, darker story arcs and more of a "sitcom" feel (in the best way possible) where the focus is more on the characters rather than the adventure. The episodes vary greatly in terms of theme, you could have an episode where you're laughing every 2 minutes from the sheer silliness, or witness the most psychologically gut-wrenching thing you've seen in a long time. You can't go wrong with either, and both have a bit of a rougher first couple seasons before they hit their stride.
As far as more recent trek, I enjoyed pretty much all of them but I would say strange new worlds is probably the cleanest and best for a new person. Lower decks is absolutely incredible but is more of a love letter to all the previous shows so you won't get as much out of it as someone who has seen everything.
- I'd also point out that TOS, TNG, Lower Decks, and SNW are primarily "monster of the week" format while DS9, VOY, Discovery (and maybe ENT? Can't remember it) have some monster of the week episodes but are more serialized stories with long story arcs. I like them all but some people prefer one style over the other.
  Something else to check out might be The Orville. Its not tied to Trek at all but it's about as close as you can get to a modern TNG.
  
  Absolutely agree with you both! Didn't know what to expect from the Orville but I was so pleasantly surprised. A little TNG with some Lower Decks like humor sprinkled about. I'm biased though, love some MacFarlane .

to be perfectly honest, order doesn't really matter. There is a small amount of interplay between TNG and DS9 and that's about it. Watch it in whatever order fancies you, as long as you don't watch Enterprise first because it's high level of boredom might turn you off
Trust me when I say that if Trek strikes your fancy, you probably will want to devour the rest
personally I would suggest starting with TNG, that one definitely qualifies as the "most universally loved". Plus, if you liked Lower Decks, then TNG-era Trek is likely to be your jam anyway
after TNG, watch DS9 and Voyager in whatever order you want. They ran concurrently originally, with DS9 having started a couple years before Voyager. You can watch the TNG movies anytime after finishing TNG bearing in mind that First Contact has minor consequences in DS9 (you will mainly notice a uniform change that coincided with the release of that movie)
watch the TOS movies at some point! they are much easier to get into than TOS proper. Just bear in mind that the even numbered ones are generally better liked than the odd numbered ones.
- I've been into Trek since TNG, but I had a buddy who never was, and decided to just look at episode/movie descriptions and watch that episode. I think he said he liked it when the description was vague or generic looking, and those episodes he liked.
  Anyway, kind of a roulette way to watch, but yeah!
  Also, try award winning episodes, like "The Inner Light" (TNG), might give you something!
  
  +1 for Inner Light being a great way to get people into Trek!
- That Enterprise shaming…
  
  It's just such a long road...
- I agree with you but I want to add that how Enterprise developed was a damn shame.
  It was shaping up as one of the best series, the thirst for wonder and discovery, the curiosity and human ingenuity. It was one of the series closest to the original ST spirit.
  Then 9/11 happened, and it turned into a weird mess with time travel ,a huge war in the middle and all that crap.
  Such a shame.
  
  It started with the time travel though? And even though its a bit off now, i think how enterprise handled the xindi arc was pretty good considering what happened at the time.

I want to start with the earlier series but not have to watch all of it!
Why the rush?
Are you cramming for a test?
Why don't you want to watch all of it?
the most universally enjoyed Star Trek series' and movies?
People are different, opinions differ. There is no correct answer to this.
My opinion:
Best OG movie: Star Trek 2
- I was wondering the same thing, especially because TOS is my favorite!! It's only 3 seasons long, and for me each episode is an absolute gem.
  Totally agree on Star Trek II being the best movie. TOS S1E22 explores the backstory of the film's villain.

LD and SNW are fine places to start.
I started with Voyager because that's what I saw on TV when I was a kid and the nostalgia was strong. If LD and SNW are catching your attention for whatever reason, go for it. IMO, the benefits to watching Trek series in any particular order is marginal unless you are going to become super into the lore.

@zac@lemm.ee
I'll give it a shot for TOS.
Top 10, plus bonuses:
Space Seed. Great episode, plus backstory for The Wrath of Khan, which is my favorite ST movie by far.
The Trouble With Tribbles. But they're cute!
Mirror, Mirror. The original mirror universe ep. Bonus: The Enemy Within.
Amok Time. Spock, amok.
Arena. Gorn wrasslin'!
Balance of Terror. Those Romulan dastards. Bonus: The Enterprise Incident.
The Doomsday Machine. Great ep.
The City on the Edge of Forever. Best overall ep?
The Devil in the Dark. Personal favorite.
The Naked Time. Great ep, much Spockage.

This might be an unpopular opinion, but I'd start with Wrath of Khan (movie #2). Watch through Voyage Home (#4). Then watch #6. These are designed to be approachable. ::: spoiler (Incidentally, the Stealing the Enterprise scene in #3 is one of my favorite sequences in all of Star Trek) :::
Then watch TNG -- you can start on season 3. You'll find more depth than you found in the films, both with characters and plot, at the cost of needing to pay closer attention.
If you like it, you can jump back to TOS (you'll already know the important characters from the films), or finish TNG, or try DS9. By that time, it'll feel more like just wanting new Star Trek to enjoy.
Stay away from movies #1 and #5 unless you already know you're a fan. There's value there, but it'll be hard to see unless those glasses are already rosey. ::: spoiler What does god need with a starship? :::
Edit: I've been a lifelong lover of Trek, but as I think about it, this is probably how I first got into it as a much younger person. I don't know how many people actually start from TOS S01E01.
- We had Wrath of Khan on Select-a-vision when I was growing up. One of my first introductions to Star Trek other than snippets of the original, I was a kid. It terrified and fascinated me, definitely sparked my love for the series.

There is ‘Where should I start?’ In Community Info the old subreddit. It laid out the different options for viewing order. Elsewhere, many Trek sites publish ‘best of’ lists that can provide suggestions for compressed viewing.
Our mod at our new home here (who was the mod there) is still working out how to create access to some kind of linked community info resources.
In the meantime, keeping in mind that TOS, TNG, Voyager and SNW are episodic, there’s no harm in dropping into episodes in any order and seeing what you enjoy. It’s the way many of us got into the franchise in the days of syndicated reruns.

My favorite Stark Trek show is Deep Space Nine. I think it's good starting point.

Loved Final Space. Old Trek is not Final Space. It's a lot more like Bob's Burgers. Things happen in the episode, but if you miss one you're not un-prepared for the next one. TNG they started doing more 'to be continued' episodes and had more "lasting effects". DS9 continued tradition and kept and underlying plot episodes sprinkled through the seasons, getting much closer to Final Space storytelling. Voyager and Discovery follow the Final Space storytelling, large plot with smaller stories getting us there. Beyond those I've mentioned, I did get in S1 of Picard and it follows "big plot" as well.
Pluto has channel that runs nothing but TOS and TNG, maybe fall asleep to it? Put it on while working or exercising?
- Pluto has a Voyager channel also! So plenty to watch if the others are on an episode you've seen or lost interest a bit.

DS9 is how I got into Trek after catching re-runs while working a security night shift. After that, I bounced around all the different shows / movies. Didn’t really follow any set guide or watchlist. I’d recommend starting with whatever show appeals to you most and going from there. Don’t overthink it. Just watch and enjoy.

If you got into the show, wouldn’t you end up wanting to watch as much of it as possible? Just watch the show. If you like it, keep watching. If you don’t, stop.

If you liked Lower Decks because it's also funny... Maybe start with The Orville. (It's not really Star Trek though)