The first step is to take a Hunter Education Course, this is important to keep you safe in the woods. Check to see if your state offers one if not you could try our states on-line course here.(free to take the course)
Official Indiana Hunter Safety Course | IN Online Hunter Safety Course
As far as a shotgun or bow, the bow takes a lot of skill & practice but the shotgun is much more versatile, it can be used to hunt every thing from birds, squirrels, rabbit, to larger prey like turkey & deer. The only draw back is it can be rough on the young hunter because all shotguns have a good recoil or kick to them. This is to say when you pull the trigger & the shot charge going through the barrel will push the stock of the gun into your shoulder hard. The smaller or lighter the charge the less the kick. That is why a lot of young hunters start off with a .410 shotgun, but if you can handle a larger gauge shotgun it would be better to start on that from get go.
The game you start on depends on your skill level, most hunters will start with rabbit, squirrel, dove, to learn how to be quiet, & concealed, or stalk, & shoot. One of the most overlooked parts of hunting is the clean, safe processing of your harvest. We as hunters are not out just killing for sport we are taking of a nature made product, to use this harvest on our tables. This is another reason why hunter-ed is so important.