Suggestion:
First, it would be best if you did open a checking account, and maybe even a savings account too. I would suggest to go to a credit union. Bank accounts are so fundamental and they show lenders how you are able to pay them. You don't look very reputable when bills are always paid money orders or other forms.
After, at the least, a checking account has been opened, apply for a secured credit card with the credit union.
Find a well-known credit union in your area that offers credit card accounts.
Lastly, if you have had cards stolen frequently in the past, you need to be more vigilant, careful, and secretive about your personal information, including the items that numbers are on, like cards or documentation, and when providing personal information yourself.
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To raise credit score
1. Always pay on time or ahead of time.
2. maintain low balances on credit cards
3.To boost your score: Don't charge anything for at least 60 days before applying for a loan
4. keep your total potential debt to earnings load low – If you have a card with a $15000 credit line, you may ask them to reduce it to something more realistic, like $5000.
5. You should have a recent history of both installment or term (Car or house loans) and revolving credit.
6.To boost your score: Don't close unused accounts when you transfer debt.
7.To boost your score: Consider opening another credit-card account or two, or taking out a car loan or small bank loan.
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http://www.bestcreditrates.net
Without a bank account you cannot get a secured credit card. Or you can get is a prepaid card and that does not build credit
Prepaid cards will not build credit. You need a secured card.
The best place to start would be your bank. Since you don't have a bank account, I suggest you open one. If you haven't resolved the "stolen card" problem, you probably shouldn't even think of getting any kind of credit card,.
A secured card is a great option for building up your credit. Here are a couple of resouces to help you find the right credit card:
http://moneygirl.quickanddirtytips.com/raise-credit-score-fast.aspx
http://moneygirl.quickanddirtytips.com/how-to-build-credit.aspx
The best thing to do and the thing I always say is that PAY YOUR BILLS ON TIME. avoid delays