I haven’t played live in a while, but when I did, I tended to have some kind of distortion, delay, reverb, and a filter on hand. For reverb at the time, I was using a Lexicon LXP-1, which is a great little box, not really hi-fi but has a lot of character, and can still be found used for not a lot of money. All my recording these days is effectively made to be a liveset, for reverb I’ve been using mostly an H9 with the Space’s Hall algorithm. While the H9 isn’t as knobbed up as a Space/Factor pedal, it’s pretty easy to navigate and having multiple effects on the one pedal is useful.
I’d recommend avoiding sticking reverb on a stereo mix out, and rather use it as a send. Gives you a lot more control, and it’s really easy on a crappy PA for reverb on everything to make it all just sound like swampy garbage.
Wholeheartedly agree with these two points. The audience isn’t there to worry about the finer points of reverb tails, and it’s often difficult to convey those finer points anyways. I’d be primarily concerned with getting effects that work for you, based on the sounds you like, or the function and flexibility of the interface, or your preferred price point. On top of Eventide, Strymon, OTO, or TC choices already mentioned, something like the Boss RV5 isn’t a bad choice if you’re looking for something not too expensive and compact. Even something like the Zoom MS-70CDR might do the trick under the dirt-cheapiest category.
Also worth adding that dirt cheap if it can do the job in a live setting isn’t a bad option to consider. I doubt anyone is going to cry if that Zoom pedal gets broken or stolen at a venue, a Strymon Big Sky on the other hand breaks my heart just thinking about it speculatively.