22 Rimfire Benchrest Shooting competetively is huge fun.
I shot that competition for a couple of years here in Michigan.
Maybe the best place to start is to spend some time over on Rimfirecentral.com A great bunch of guys hang out there, and there's a wealth of information on benchrest shooting available there.
I can't tell you what to buy as I think you have to address what level of competition you want to engage in, then buy a rifle accordingly.
I have eight Ruger 10-22's, a few of them all tricked out for competition. I have two Martini Mk II's that are competetive at the local level, but won't win in national competition. I also have a Suhl that is accurate for most matches, but again, won't win against the the big boys shooting custom 22 benchrest rifles. For a fun rifle, that is way more accurate than most others, buy a CZ 452 or 453. I have a 452 that shot a 3/16" group at 50 yards the last time I shot it, and that was a 5 shot group. The most accurate semi automatic rifle out of the box is the TC Classic. The Ruger 10-22's will equal it for accuracy, with the addition of a WHOLE lot of time and money adding aftermarket parts.
It's a fun sport, and you can have fun shooting it at any level, local club matches, which I personally like best, or state or national level.
Ron Hoehn lives in the Saint Louis area and is a big competitor in not only 22 Rimfire matches, but centerfire also. He is in the gun making business, along with selling shooting supplies. So you could find him easily to talk to.
If possible, go to a match somewhere, talk to the guys shooting, and look at what rifles they are shooting. Then decide what you want and can afford and buy a rifle.
Martyn