Do you have a price range to stay in? You can easily spend a small fortune on high end barrels, triggers and stocks.
Or you could start with a 10/22 Tactical which comes with a heavy target barrel and bi-pod longer range shooting is what you want. I'd also think the SR-22 would except any width barrel without modification, but I can't sweat to it.
My ATI stock will not fit the target barrels without a fair amount of dremel work.