What the rifle is chambered in, isn't really that important. Any of the standard cartridges from .243 up to .30-06 will kill varmints and black bear.
Start searching the used gun racks, trying things on for size.
If the gun comes to your shoulder easily and you get a good cheek weld without squirming around, then the rifle fits.
For most of the day a rifle is a dead weight. Getting one that weighs a ton is not a good idea. The other side of that is that the heavier the rifle the less felt recoil.
Hunting often involves walking through woods or brush. So a shorter rifle tends to be a better choice. The exception is when you spend your time sitting in a blind waiting for Bambi to walk by. Then a long barrel isn't a problem.
My rifle is a Winchester Model 70 in .30-06. I've never had a problem with it that wasn't my fault.