I agree with Wirehair, stick to a bolt action. My wife had a Ruger 10/22, you cant get any sensible grouping with a semi auto, it's hard enough judging range and compensating for the trajectory of a .22 sub. We put it in part exchange for a Sako Finnfire, A excellent tool if rimfires are your thing. We also use a .17HMR rim-fire which is a c.z with no complaints.
I would agree with the other posters that using a normal factory semi at anything above 50 yards may not be to humane.
I had to have my 10/22 rebarrelled with a Shilen some 15 years ago when this sort of thing was almost unheard of. Shoots well now as does my now discontinued Theoben/AMT.
To get a semi to peform you will have to look at semi custom jobs from the likes of SYSS. No one wants to see a rabbit crawl away wounded, choice is either a cheaper bolt action or a semi custom semi.
I ONLY use semi's in .22LR but even with custom/semi customs limit my ranges. At night they are great. Be aware though that they soon clag up when using most makes of subbies. The Eley 40 gr and Lapua are the best SSHPs in this regard but even with them after 200 or 300 will require a full strip/clean/rezero.