IMO a good model 70 (Winchester) varment rifle is as accurate as any other out to 250 yards or so. And the difference then, is maybe half the diameter of the bullet.
Most of my experience is in .308 caliber, but I have both a model 70 (varmint) and a Mannlicher Styer sniper rifle. The Styer is deffinately a good rifle, but I´ve rarley noticed much difference between it and a model 70, until the distances get really long. Trigger groups and such are easy to come by for the 70, as are scope mounts and stocks.
A set trigger, self loaded ammo and practice are probably more important than price. Most rifles will shot better than the shooter anyway.
The model 70 is about 1/4 the price of the Styer. A little cheaper than the Ruger. A couple of hundred cheaper than the Savage. The money you save on the rifle you can add to a better scope.
Another tip, a good scope is often more important than an exotic rifle. If I had to make a choice, I´d put a thousand dollar scope on a $700 dollar rifle and shot better than somebody with a better rifle and a poorer scope.
A rifle that fits well, with a good trigger and with good optics is often more important than bull or beaded barrels and other exotic accurizing features.
You can argue my oppinions, but you´d have to prove it on the range.
I´ve never shot a 22.250, .222 remington used to be one of the more accurate rounds. but you don´t see that caliber rmuch anymore. .308 is tried and proven accurate. Think my next rifle is gonna be a .243 for varmint and occasionally for deer.