I think you’d be surprised how many all in one brewing units are small enough to fit in a closet and take up little space when not in use. Vevor makes a cheap but serviceable 120v system that I believe is around 200USD and is the size of a pony keg or so when not in use. Then you would need stackable buckets for fermentation.

For serving I prefer kegging over bottling. Admittedly both take up space but there are ways to dual purpose the space used for a kegerator.

I’m helping a younger coworker figure out his apartment space and budget needs so I’ll keep you (or any one interested) in the loop, if you like.