I'd recommend getting a regular credit card, but only one (so your combined credit won't be too large). Get more later when you feel more comfortable about it and know you can do it without screwing yourself.
Don't get department store or other proprietary cards. They're bad because A) you can't use them at any other store, and B) since it's credit, it requires an inquiry against your credit record, and too many inquiries hurt your score.
Also, get a card with no annual fee. An annual fee is like spending money so you can spend more money (which is why it's important to carry balances as small as possible, as interest is the same thing).
I don't know this for a fact, but I'd try getting a Visa from your bank because they'd already know your history of check writing (like how you haven't (or have) been writing bad checks, etc.). Plus by already being a customer of theirs, getting a credit card would help them make more money off of you (don't worry, stuff you buy won't cost more...they make the money in other ways).
Stick with Visa or Mastercard. They're the most widely accepted. You can get American Express or Discover, but why bother? You can't use them in as many places, and the places that do also take Visa and Mastercard.
And I cannot emphasize this enough:
DON'T SIGN ANYTHING UNTIL YOU COMPLETELY UNDERSTAND THE TERMS AND HOW THEY AFFECT YOU.
Otherwise something strange may happen, you'll be like WTF? And when you complain to the bank they'll say "but you signed this agreement, so you agreed to this."
Ben