If you don't have any current open revolving (= credit cards) credit at all, you will probably not be penalized for seeking new credit. The FICO scoring formula *wants* you to have some revolving in there.
Have you had revolving credit, i.e., credit cards in the past? If so, which banks? Did you ever "burn" them/ --charge-off, bankruptcy, settled for less than agreed.
I would get with a local credit union that offers CC's right away. They are the most reasonable about working with new creditors. If you absolutely must go with a secured card from a bank instead, look at Bank of America and Orchard.
If you're willing, you can post a summary of your current credit here, and you will get lots of advice (wanted or no, lol.) Post the info from screen 2 of the FICO EQ and TU reports, along with the Credit-at-a-Glance screen.
* Credit is a wonderful servant, but a terrible master. * Who's the boss --you or your credit?
FICO's: EQ 781 - TU 793 - EX 779 (from PSECU) - Done credit hunting; having fun with credit gardening. - EQ 590 on 5/14/2007