Most cards don't carry annual fees these days, but some do. Check to make sure. Usually the ones that do charge an annual fee have some kind of incentive program like flight miles.
If you pay off your monthly balance completely or don't use the card, there will be no monthly fee.
There's a kind of credit card for people w/bad credit histories and perhaps people w/no credit histories... I started out by being on a joint account w/my mom, so I don't know much about those things, but those kind of credit cards have to be funded in advance.
I imagine that you can get a normal credit card on your own, especially if you have a steady job and address.
Good luck.
