[White Shark]

Ruger 10/22. Move up to a .30-30 Lever action when you've mastered the .22LR. Then try a .30-06 or something similar that will give you a clean kill at distance without lifting you out of your boots everytime you shoot. All of these calibers are easily available even in small podunk towns. They are also easy to sell if you ever want to swap out for something else. They are also the cheapest to shoot in small, medium, and large cartridges.

Ruger 10/22 in .22LR
Marlin or Winchester .30-30 Lever Action (I like the Marlin)
Browning H-Bar or Remington or Weatherby .30-06
If you want Elk or larger, you might get into a .300 Weatherby Mag or 7MM Mag.