i'd go with bolt action over any semi-auto, and the .223 is a good round. i've shot a built Remington .223 with a 36x Leupold on top, and it would put 5 rounds through one hole at laser-measured 100 yds. then i'd shoot out the four staples holding up the target.
i'd go with a centerfire round. you can shoot handloads (someone else's, if you don't load them yourself). you can shoot at longer ranges. you won't have to deal with a transition from supersonic to subsonic like you will with the .22LR (unless you get those low powered subsonic rounds).
there are some very accurate .22 LRs out there, but i would definitely go the centerfire route.
Remington makes a good, accurate action. The stock trigger is also pretty good once you adjust it (and you can do it yourself). if you wanna get hardcore, you'll want a custom trigger, but you could hold off on that for a while. I don't know what else people use to really build awesome rigs. Savage is pretty good if you're on a budget, but I don't know what the aftermarket for them is like.