What are the staples of what you need to do medium sized gigs in a decent bar? I mean, I know you probably need a mixer, loudspeakers on a stand, maybe a separate bass cabinet, but what else, and what kind of mixer, what kind of power, etc., do you need?

Currently I only have my instruments and a D.I. box for my acoustic. Never had to do anything but plug into other people's stuff. Talking to a few guys about starting a band, but they're all in the same boat, so basically none of us have any equipment at all, no speakers, mixers, big cabs, big amps, cables, nothing but our instruments and the immediate equipment for those.
You could just get guitar amps, bass amps and a PA for your vocals. You don't have to get a mixer; just set the levels by ear.