If I pay my balance in full that month, do I get charged interest? And what is the best credit card for a person who has no credit, can't make but minimal purchases and payments throughout the year, but wants to get credit?

Most cards have a grace period, so if you pay in full by the due date you will avoid interest charges. Take a look at the Nextcard and Getsmart cards in the browse section of CreditCardmenu.com
These cards offer customized interest rates based on your credit history. If you are not able to obtain one of these products you can look at a secured Orchard bank card to start building credit.