Part of rebuilding your credit is proving that you can pay your bills on time. If your bad credit episode left you without any credit cards, you'll have to open new ones.
Since your credit score is sensitive to negative credit report entries, avoid randomly applying for credit cards. Several credit inquiries will make it harder for you to get a credit card.
Financial Globe's Score Match gives you a list of credit cards based on your credit score. The site also indicates the approval rate of the credit card, giving you a better idea of whether your application will be approved.
If you don't know your credit score you can use a free FICO score estimator to get an estimate of your credit score.
Whether you have good credit or bad, it's always best to choose credit cards based on their features and not your need for credit.