If you are talking High Powered shoots, than the NRA or CMP websites will have the appropriate info. Most ranges have 3 position shoots and almost any rifle is welcome. For timed events, the norm is for bolt guns to receive some additional time, 15 seconds or so. There are so many folks that shoot from the bench only these days that keeping your 3 position skills tuned can really make a difference in competition or in the field. For most competition shooting a heavy barrel is most desirable. These are a couple of mine. 1st a Bushmaster DCM, 2nd a Howa 1500 .308.
Now, if you want a cheaper type of competition shooting, Military shoots are great. The rules of each shoot will specify the types of Military arms allowed.