30-30 .308 30-06 .243 is what I use .270
Good advice for you, here. All of those calibers are easy to find and do the job well.
.308 is a dandy caliber for deer and is easy to find in any place that sells ammo. It's got an added bonus of having some less expensive shells produced for it if you want to target practice. (These won't do for hunting, though).
Here's my take on each:
.243--light kicking and great for youth/newer hunters who aren't used to recoil. Not really thought of as a cartridge for bigger animals like elk, though. This is an ideal cartridge for my home state of Kansas as it handles deer and works for coyotes in the lighter loads.
.308, .270, 30-06--all of these perform about the same. Capable for black bears and elk, if you are sensible with your ranges. Personally, I like the 30-06 because it offers more selection when picking shells--more bullets and loadings. You'll have no problem with the others, though. Most people can handle a 30-06 recoil.
.30-30--an old classic but shorter range than the others. They'll easily outperform it. Keep shots under 150 yards for sure especially with open sights.
Now here's what it's got going for it: it shows up in lever actions that are slick, light, and fast handling. In woods and heavier cover or anyplace where quick shots and short shots are the norm, the guns built for this cartridge are normally perfect. A Marlin 30-30 or similar gun is a great piece to be carrying in the woods .
Personally, here's what I'd get as a first rifle--30-06, bolt action. It's very versatile and hard to go wrong with one. It'll do just about anything you ask with the right bullets.