First of all, it's good that you are expressing a desire to rebuild your credit because too often people simply decide credit card use isn't for them and try to make do with a bad credit score. Doing so obviously forces them to pay unnecessarily high costs on loans and insurance premiums, not to mention the fact that they have a harder time getting approved for a plethora of things, including home and car leases, mortgages and even jobs that require security clearances or the handling of money.
With that being said, your best bet is going to be a secured credit card, for a few different reasons. For starters, no matter how bad your credit is, you can get approved for a secured card. This is because they require that you place a refundable security deposit, which acts as your credit line, both protecting the card’s issuer in the event that you default and precluding the need for high fees.
A secured card's low fee structure not only makes it easier to pay all of your bills on time, but it also gives you the option of simply locking your card in a drawer and thereby building credit without the temptation that comes with making purchases. You see, information about a credit card account is relayed to the major credit bureaus (Experian, Equifax and TransUnion), regardless of whether the cardholder makes purchases or not. As long as your account is in good standing, this information will be positive and your score will gradually rise.
While the gains won't be as pronounced as if you were making purchases and on-time payments, this is a great option for people who’ve run into trouble in the past and are nervous about repeating their mistakes. What’s more, you can also add to your security deposit over time and, in doing so, increase your available credit as well as your credit score.
You should be able to move to an unsecured card after about a year of responsible secured card use. (That means if you do make purchases, you must make them on time!)
Hopefully that helps!