My standard live mixer for LITERALLY decades has been a 1st-gen Mackie 1202. They're built for maximum abuse, very much the "takes a lickin', keeps on tickin'" Timex of mixers. Small, too...one can sit on a vinyl album cover and still not take up the whole thing. And yet, you get two AUX sends and returns, inserts on strips 1-4, four stereo strips, tape I/O...it's the small mixer that pretty much redefined what those were back c. 1990 or so.
I haven't played live much, but so far I've always just plugged into whatever system was provided at the venue. Either into a mixer or into a DI. I have a box of various cables and adapters so that I can plug into anything that is offered.
However I also have a portable Behringer PA system which I bought very cheaply from a neighbour (it was a steal, don't tell him) and I take this to our monthly local synth meetups. It's got great and loud enough sound, some FX, and is a very sturdy package when packed.