Before even considering a credit card, check your income. If your surplus cash at the end of the month is always near zero, any credit is going to be hard for you to repay. This also means that you will be tempted to buy things near the end of the month on the credit card. This will result in less cash next month when the payment comes due, and that is how a vicious cycle of unending debt begins.
For you the best card is no card. However, if you feel that you need a credit card for things like car rentals and genuine emergencies, get one card and put it away until you really need it.
Start your search for a good card by realizing that your debit card is not a credit card. If you spend beyond your checking balance, overdraft fees will kick in. You will regret it in a hurry. Not very many accounts these days return checks until you are way overdrawn, but the fees still apply.
Sort through the applications that come in the mail. Look for a card with a fixed low rate. Low introductory rates will expire within the first twelve months and a higher rate will be applied to outstanding balances. This will make for higher payments and possible financial hardship on you.
Any card that costs you more than 15% is too high. It is better if you can get it into the 10% to 12% range. Cards that offer cash back are good, but not at the expense of higher interest rates. Read the fine print.
Citibank and Bank of America tend to be two cards that are not too quick to pull the trigger on rate increases. They also work with customers to keep rates manageable if you have minor problems arise. Chase tends to have a short fuse in this area and is not flexible about fixing it, but will sometimes offer a great rate as long as you never have a late payment or a spot on your credit report.
Look for cards that offer better deals to seniors. This can sometimes keep you out of trouble by having room for a mistake or two in the fine print.