Meh, chords are easy (which is not to say they are unimportant!) Unless you are playing Freddie Green, of course, in which case they are a nightmare (that style of big band chord playing is deceptively hard). Other than that, just do what piano players do - play the third and the seventh, plus whatever tensions you feel compelled/are instructed to play. Let the bass player get the root. The fifth is boring anyway, so just leave it out. This is PARTICULARLY true if there is a piano player in the group. He's got 88 notes he can play at any one time, and he is probably going to want to use them. Just stay out of his way, don't play too much, and pretty soon you'll be so busy gigging that you won't have time to post questions on the internet.
Well, maybe not, but as a former teacher of mine likes to say (who would know better than anyone, as he is constantly gigging), "you'll never get hired because you can solo - you get hired because you can groove."
And though my manner may be flip, I'm serious - all you need to play 75% of the time when comping (accompanying) in jazz is the root and the seventh. Tensions are nice, but they're just filler. Try to keep it down to one tension at a time unless you've got a good reason to play more (like it is written in the chart, or that big accent at the end of the melody for Stolen Moments) Same for the root and the fifth. Sure, they are an essential part of the chord (well, not the fifth - in jazz he's just the poor abandoned step child who no one likes that much), but the bass player is going to hit them anyway, so why would you want to worry about them? It's the third and the seventh which carry the function of the chord, which is what you need to worry about the most.
When your comping behind someone else's solo, playing more than the third and the seventh will just get in the way of their thing (at least, if they are any good). Also, you'll get in the way of the bass player, if SHE decides to do anything interesting - which you hope she will! The root and the seventh are the notes which define the function of the chord, and as often as not (more than that, actually), when you are substituting a chord it works because it still has the third and seventh of the original chord.
Take, for instance, the infamous tritone substitution. This is the substitution of any dominant chord with a dominant chord a tritone away. It works particularly well because the third and the seventh of a dominant chord forms a tritone. So you move the root an the fifth by a tritone, but leave the root and the seventh (which, being a tritone, is the main sound in that chord). Of course, they invert - the third is the seventh, and the seventh is the third - but they are the same notes. The other fun thing about a tritone sub is that all those natural tensions in the original chord (the ninth and the thirteenth) become altered tensions in the sub (a sharp or flat ninth, or a sharp 13 - and of course the sharp 11 is actually the original chord's root note!)
You can play more, of course, but most of the time if you just keep yourself to the third and seventh while keeping solid time, other players will love playing with you because you are leaving enough room for them - and there is nothing musicians like more than having enough room for their own ego!
So practice being able to play the third and seventh of any chord on site, and just get in the habit of playing just that unless you have a reason to play more. Also, try to work on being able to voice lead between them. Usually that will mean the voice (i.e., the string) which was playing the third should be playing the seventh on the next chord, and vise versa. At least, when you are playing a ii-V-I they will, but you will be playing a LOT of ii-V-I's if you are playing jazz, so it's a good place to start. Most of the time, if your doing this it works well to just play them on the G and D strings. Every now and then, add a tension (a 9th, 11th, or 13th) on the B string. Don't get stuck in a rut with that, but most of the time that will do the trick.
Obviously, you don't want to do this 100% of the time, but it is almost always appropriate, and seldom inappropriate. Hell, it works in a lot of rock stuff too. If you get that down, you're comping will be light years ahead of most of the guys whose recital's at Berklee drove me to a decade of all but hating jazz. Too many damn notes in their chords - it just sounded muddy.
Light
"Cowards can never be moral."
M.K. Gandhi