I prefer the Savage with Accu-trigger over the American.
I shoot a 30-06 Savage regularly. I have an American 30-06.
I am beginning, in my advanced age, to like lighter recoiling guns. 243 is an excellent caliber. I have taken elk with it.
I think that any of the budget rifles (Savage, Marlin, American...) in any of the normal "deer" calibers, will be more than sufficient to take white tails. The problems usually start with the $59 scope that won't hold a zero so people think it must be the $300 rifle. I advocate buying a cheap rifle with QUALITY rings, bases and scope. The rifle model is more about aesthetics but there is a major difference in triggers. There are some Savage rifles, I own two, with HORRIBLE triggers. I took both to a gunsmith to do trigger jobs and they are now tolerable.