For non-match rifles, CMP Sporter.
If you really, REALLY want to shoot smallbore 3P, but aren't ready to dive into an Anschutz, look around for a Walther KK100. My little brother used to shoot one, and it will shoot darn good. Not good enough to WIN, but close. I shot it (the rifle, not smallbore) a few times and it would cut one-holers at 50-yards prone as long as I did my job. (I'm a Master-class Highpower shooter myself, FWIW.)
And the accuracy thing is really crucial. Like trying to practice for a Highpower match running junk Lake City ball. Just don't buy into it; it's more frustrating than it's worth IMO. My experience is that the best way to get where you're going is to just give up and spend your $$ up front. Lots less aggravation.
NRA Master, Highpower Rifle, Across-the-Course
NRA Expert, Highpower Rifle, Mid-Range Prone