I'm constantly cleaning. I live alone in a 100+ year old building. It's no exaggeration to say that there's a coating of dust moments after I get done dusting.
I use a microfiber duster for daily cleaning and a heavily diluted mixture of water, vinegar, and soap for deeper cleaning.
The only thing I can think of, but haven't tried, to minimize dust accumulation is to run a humidifier. That should theoretically give the dust particles something to cling onto and be less prone to becoming airborne as you move about. Perhaps a daily water misting from a spray bottle could work - I should give that a try.
I have an air purifier in my bedroom. It doesn't do very much. I don't really understand how they're supposed to work anyway. There's no way it's going to suck in dust from the other side of the room. I wonder sometimes if it actually makes things worse. I use it mostly for the white noise to sleep with.