I've personally been behind all of the chassis that have been recommended. Here is my opinion. 1) McRee: absolutely great chassis system- drop in and go. They are easy to adjust and real comfortable. (I've personally owned 2 of them). 2) XLR: While I have never owned one, one of my buddies has one and its a great chassis. My absolute only complain is the round hand guard up front. And that simply from the prospective of shooting off barricades and such in comps. 3) Rock Solid: such a simple great design and an almost perfect chassis for comp type shooting. Again drop in, easy to adjust, and then your off to the races. 4) KRG: while I admittedly haven't spent as much time behind this chassis as I have the rest of them and I've never been behind the newer Xray; the w3 is one of my favorite in stylistic features and overall performance. Yes, yes.. this is not under 800$ but nor is the AI chassis and that I would stay away from, its truly not for everyone. It really didn't fit me. I'm 6'0-6'1 180 lbs and I have arms like a trex. Idk what it was about AI chassis but I just did not like them (however, to each their own).
If it were me in that price range, I would honestly take a look at Rock Solid and McRee for competition style shooting and the XLR for your all around stock. The KRG Xray I can't speak to much about but there is a solid thread on here about it in which I'm sure you could find plenty of info.