Theres 2 completely diferent scenarios and applications for a rifle, for ground hogs in fields a bolt action hands down, but for deer hunting i run 2 diferent rifles a bolt action for when i'm going to whatch fields or cuts or hunting in marshes, but if i'm in the thick stuff and swamps still hunting i love a light wieght lever action but mostly its a personal preference thing. If you want the best of both worlds consider a BLR or Savage 99 they have the handling of a lever action but are often capable of matching a bolt action in the AVERAGE shooters hands for accuracy in hunting conditions.
For biggame I think it boils down to what you shoot best and what feels more comfortable to you. After all, for deer you should only be making one shot anyway. Varmits or prarie dogs are different, but again, it comes down to what you personally prefer.
I once read a book on deer hunting where the author prefered and was advocating the use of pump action rifles. His logic was that you can make a faster follow up shot without taking your cheek off of the comb. Again I think it comes down to what you as an individual prefer.
You must keep in mind that from the late 1800's until the end of prohibition that most hunters were using leaver action rifles. This is why the Savage 99 is still held dear to many hunters hearts. It really was not until after the first world war that the bold-action rifle only started to be adopted slowly by hunters.
As the allure of hunting big whitetails becomes more and more a passion for many, we are finding that the recent (historically speaking) popularity of hunting deer from a tree stand is becoming the way to do it. I'll make no statement either for or against that technique here. This will be simply an essay on what I feel are some outstanding rifles for tree stand use.
Before we go even one more step, let's all remember that safety is first and foremost for anyone wanting to hunt...