I would like a credit card without annual fee, but I don't have a credit history. What do you recommend?

You can choose one of the credit cards for limited credit to make your credit profile better. Or you can consider secured credit card. Some card offers have no annual fee and pretty nice rewards programs. Thus, you may save more money than spent on the security deposit.

We can recommend you start with secured credit cards. These cards require a security deposit paid upfront. A secured credit card is a good way to build your credit history as it reports the account activity to major credit bureaus. You just need not to miss payments and pay off your balance. After that, getting approval for an unsecured card will be much easier. For example, you may consider the Merrick Bank Secured Credit Card. This card can help you build credit, since your account activity will be reported to all three major credit bureaus. The amount of your deposit determines your initial credit...

Starting credit history from the very beginning is always better than improving it and credit card issuers are not too captious.Look into credit cards for those with limited/no credit history: these cards are created for newbies. The cards have quite high APRs and fees. However it is possible to find a card with 0 intro APRs or without annual fee. Also some cards offer bonus programs: you can earn points or cash back on purchases you make.If your son wants a bonus credit card, Chase Freedom® Student credit card is not the best option as it has no bonus. The only you get is $20 Good Standing...