Once you pick your round/cartridge and buy your new rifle I'd try at least 3 different big name ammo producers and buy their very affordable boxes. I'd try Remington cor-lokt, and Hornady Whitetail lines (to name only 2). If they shoot well in your rifle you are ahead of the game with easily obtainable and inexpensive ammo.

Be prepared to try at least 4 types to find what your rifle likes, and you may find the best stuff on your 6th or 7th box. Sounds like expensive trials, but hey, ... shooting is fun!

Good luck. BTW, either the 30/06 or 308 will serve your purposes. And, just for fun, so are about 10 other cartridges... your choice.

FWIW ... the 30/06 would be hard to beat for availability of guns, ammo, and components.