I live out west and we have all kinds of terrain, from open fields to heavy cover in the forests. I have a Browning A-Bolt .30-06 that gets the job done in the open fields and semi wooded areas. For thick cover my Marlin .30-30 is perfect.
You can readily find ammo in these calibers anywhere you find yourself in the USA (and perhaps the world).
You might want to check out the prices of ammo in various calibers before selecting a rifle. Some ammo for some calibers is priced sky high while for other calibers the ammo is reasonably priced. Go to Cheaper Than Dirt - America's Ultimate Shooting Sports Discounter
and take a look for yourself.
Ammo price should not be your only consideration when buying a rifle. I never go with magnums in any caliber. That is just me though. I find smaller calibers get the job done very nicely. My suggestions in calibers are: .243, .257, 7mm-08, .30-30, .270, .30-06 None of these are magnums and they all get the job done well.