Your best bet is to call a good, local lender and discuss your credit with them. Normally, you don't have to have your credit card completely paid off in order to have good credit. The key is to have a balance that is lower than 1/3 of your available credit. As long as you don't have late payments, you should be in good shape.
A lender that I do a lot of work with is Cherie Bowen at Academy Mortgage. If you call her, she can take some information from you over the phone, pull your credit and then let you know where you stand. She will guide you, if needed, or she will let you know what you qualify for and what programs are available.
At this time, there are programs that will grant you 3% of the purchase price of a home for your down payment as a first time homebuyer. Cherie can give you more details of the program --- I'm a Realtor, so the loan and financial side is not my specialty!!
Once you talk with Cherie - or any lender you want - if you haven't already started working with a Realtor to find you homes to see, give me a call! I will be happy to email you homes that are available and have you choose which ones you'd like to view in person.