The 30-06 is a great hunting cartridge, because there are tons of different types of ammo for it. For whitetail, I'd say go for 150grain bullets. They weigh plenty enough to bring down the whitetail, and by being that light, they will travel at almost 3000fps, sometimes more.
As for ammo, I love Winchester Ballistic Silvertips (the nylon ones, not the old big silver tips). I also like federal nosler tips.
I don't know much about your rifle, but the pump action is probably one of the most reliable actions out there. Remington is known for making very good barrels as well, so I'd say the Barrel + Action + Caliber = One awesome whitetail gun