Highpower has two major rifle categories:
Service Rifle and Match Rifle.
Service Rifle is the AR15 in A2 configuration (fixed stock, carry handle with sights, 20" barrel), M1 rifle, or M14 rifle (or its civilian clones). Nothing else is eligible. In this category, the AR15 is king.
Match Rifle is any repeating rifle with a magazine capacity of at least five rounds, iron sights, and the ability to rapidly reload. Your Mosin Nagant would fit here, though it would not be competitive even if you are a High Master. Custom made bolt actions with special match sights, stripper clips or detachable magazines fit here. Customized AR15s with long barrels, adjustable stocks, and special match sights also fit here.
If you are serious about competing in NRA Highpower Rifle, the first question is which category of rifle you want to use, service or match? FYI, both categories shoot in the same match. There are no "service rifle only" NRA matches. CMP is another story but doesn't count for now.
If you want to shoot a service rifle, buy a National Match AR15 and call it a deal. Don't bother with the M1 or M1A.
If you want to shoot match rifle, you can start with your Mosin to get your feet wet then eventually decide to build a bolt action or semi auto match rifle or switch to service rifle.