I am already a customer with a family plan with AT&T. I recently sent my cell through the washing machine on accident. The sim card still works, I have it in my mothers phone right now.
You can buy any unlocked phone that AT&T supports and simply put the sim card in. I would suggest buying a phone online because buying it from the AT&T store will be more expensive and they may try to get you to buy a new service plan. Try DiscountWholesaleBargains.com for a large selection of phones.