"...for this type of shooting..." For what type of shooting? The target shooting world is about as varied as a sport can get. There is something for everybody.
Each course of fire has its own rules for what rifles can be used. Some use heavy barreled, single shot, .308, bolt actions with iron sights only and specific ammo. Some are any rifle-any sight-any ammo. Plus .22 LR and black powder target shooting. I've never seen a list, but the DCRA covers most of 'em.