Look at the .22 hornet specially if you reload, if not go with a .223.
If you go with a Hornet look into the NEF single shots, thats what I have and it drives tacks. What I like about the NEF is it has a 1 in 9 twist which will stabalize heavier bullets. I load mine with 50 gr nosler balistic tips. Most all .22 hornets have a 1-14 twist which barely stabalize a 45 gr bullet.
And you can get other barrels for the NEF and they are pretty cheap and accurate enough to 200 yds some much further.