You were born on U.S. soil. That makes you a citizen. What registration are you talking about? Most FFLs in most states just need a driver's license to make sure you are a resident of the state where you are making the purchase. A few states like CA, NY, NJ and Illinois may put you through hoops for something like a firearms owner ID.
You can pick up a used .22LR rifle for a decent price at many gun shops. .22LR is very cheap to shoot and you can enjoy many hours becoming a marksman with little impact on your budget.
By getting registered I meant getting a permit. Sorry, got myself mixed up in there.