Good rifles to own for target shooting?

I'm not sure what caliber you'd like for target shooting. You've mentioned another .22 and the Mosin. The two most accurate guns I own at distance is a Rock River AR15 with a 16" stainless bull barrel, and my Ruger M77 in .25-06. The Ruger has a terrible trigger though. I've just gotten accustomed to it. The RR bull carbine is a beast.