Small game is good to start with. Most of us started with small game. I started with squirrel when I was five or six. A .22 rifle or a 20 gauge shotgun would be a good starter.
If I was you, I would find a mentor, determine what you want to hunt, and then find out the game regs in your state for seasons, bag limits, and in some cases weapons restrictions. If you have problems finding a mentor, you might inquire to your state's wildlife agency to see if they have a program.