If you're an absolute starter, then a good .22LR is the best bet. They're great for getting to know how to shoot well and are a lot of fun at the range. They're also great for small game like squirrels, rabbits, and various other critters.

If you're ready for something more, consider a .243 from Savage or Remington. The recoil of that cartridge is pretty light for a centerfire, and it works very well on deer.