Just some thoughts, if you are stalking there is a larger chance you have to take an unsupported shot. So a follow up shot may be more important. An auto loader is going to give the guicker follow up shot, mainly because you can usually pick up another good sight picture faster. They tend to have a milder felt recoil.
I tend to use a heavier bullet 200 grn., less chance of large deflection on a twig. Shots are likely to be close, less than two hundred yards, depending on the lay of the land. So exceptional accuracy is less important.
I have an old Remington model 8 (that is older than I am) in 35 Remington. About the same FPS as a 30 30. I kind of love this old rifle.
I'm thinking about buying a BAR or maybe a Bushmaster. I'm trying to decide if the larger bullet weight often available for the 30 06 is worth possible feed problems in the longer action or if the .308 is the better choice? I have an extra scope in 6x42 I'm planning on mounting on it with see through mounts. I have the feeling my old Model 8 may be on its last legs. I kind of have the .308 and 30 06 ballistics imprinted on my brain, so it is likely to be one or the other.
I'd check out the local pawn shops for binoculars.