Go to your Credit Union and get what I believed is called a "secured credit card". With a secured credit card, you put down (out of your own pocket) a spending limit and of course, you still have to make payments on it like a regular credit card. It allows you to build your credit up (it still gets reported to credit report agencies: Equifax, TransUnion, Experian) while not overspending because you have to put the money on it from your wallet.
Honestly, I wish I had of done the secured credit card route instead of taking up that Capital One credit card at age eighteen. -_-
Once you're ready to "grow up" in terms of credit cards, get a Visa via your Credit Union.
Whatever you do, keep good on your credit because credit seems to determine so much these days.