Rifle caliber and what game you plan on hunting might help us with assisting you in your search.
Also, no 2 rifles are a guaranteed match. One Browning might like Federal Premium, another might like HSM. You'll just have to try them out.
My 2 A-Bolt II 7mm RemMags both liked the Federal Premium P7RK ammo, which hasn't been made in over a decade. I have several boxes still sitting in the safe, since I have been handloading, but am not willing to part with them.
You will have to try a few to figure them out. In the meantime, shooting all that ammo will give you alot of brass to load up for when you do start handloading.
If you have a Browning in one of the 7mm calibers, it has a 9.5 twist, and won't be of much use beyond the 168 grain bullets.