Here is what I believe to be the definitive answer for maxing out your library on 4 inputs:
- Gaming PC/Steam Deck - you'll have access to a sprawling library of games from all generations and can even emulate console exclusive games from previous generations. The reason I'm not recommending an Xbox console on this list is because basically every current gen Xbox One (+ X|S) game is already on PC (as are many OG Xbox and most Xbox 360-era games), GamePass is an option if you wanna play some OG Xbox/360 games legally, and emulation can get you any games that aren't available otherwise. Sony is also making many recent PS5 exclusives available on PC now with more to come.
- Nintendo Switch - it's got a kick-ass library of exclusives, almost every Wii U game has been ported over (minus like 8, I think?), they've been remaking/remastering a lot of older games and are reportedly going to go hard on that for the remainder of the Switch's lifespan, and with NSO it has a respectable library of retro Nintendo and Sega Genesis games if you wanna go the legal route.
- PS4/PS5 - A PS5 would be ideal for maxing out your possible library size, because it can play any PS4 or PS5 game; however, there also aren't a ton of PS5 exclusives at this point in time, PS5 games are being ported over to PC faster than PS4 exclusives, many recent PS5 games are also on PS4, PS4s are cheaper, and the PS4 can be jailbroken. There's a case to be made for getting a PS4 instead.
- Modded PS3 - Especially if you can track down a phat model with hardware back compact support, you can load up a HDD with games and play the entire PS1, PS2, and PS3 libraries.
With these four, you should be able to play essentially any game ever made. You will have...
Official hardware support for:
- PlayStation
- PlayStation 2
- PlayStation 3
- PlayStation 4 and/or 5
- Nintendo Switch
- PC (Astonishingly huge library)
You will have the (paid) option of legal software support for many of the best games from:
- NES
- SNES
- Sega Genesis
- Game Boy
- Game Boy Color
- Game Boy Advance
- Nintendo 64
- Xbox
- Xbox 360
You will have the capability to emulate anything from Atari 2600 through to some Nintendo Switch, including Xbox, Xbox 360, GameCube, Wii, Wii U, arcade classics, and many, many more.
IMO, this is the best way to max out the 4 ports on your TV. You can also get a PS Vita and mod it for PS Vita + PSP games, and a 3DS modded for 3DS and NDS games. They don't need to be plugged into your TV, so they weren't included on my list of 4, but they are both excellent handheld consoles with great libraries.