Venues, like rehearsal studios, generally provide kick, a couple of toms, hi-hat and snare. Most drummers prefer their own snare, and cymbals, and often that includes their own hi-hat cymbals. A comfy seat is a personal choice too !
So, you could get away with those if you were sure of a 'back line' kit.
Not expecting any kit on site, a kick drum, snare, ride and crash cymbals and hi-hat would do. Not forgetting seat and sticks, of course ! If space is a problem, that's it. If not, use a small tomtom as well.
I've worked with several bands with electronic drums, and when played by a drummer who knows what he's up to, they can sound just as good as an acoustic kit. Often better - think about the fact that you could get away with, say, one tomtom, which could change sound at whim.
Some of the guys I work with have 2 or 3 kits, with different sized bass drums, so can tailor the kit to the gig. But cymbal wise, hi-hat and ride, and often a crash, are there every time.With the appropriate stands- don't forget the stands !