General advice: It takes 90 days to establish a credit score. You absolutely need the credit score to qualify for a loan. It is a good idea to establish 3 credit sources. One credit card will not do enough to establish a score. A bank credit card, a gas card and maybe a specific store's card (Kohl's, Macy's, Target, etc.) would work, but you have to use them and show that you can charge something and then pay it. It's not enough just to have it if you don't use it. Do not buy anything large (like a car) until you talk to someone if buying a home is your priority. While car payments can help establish your credit, it also reduces the amount you would qualify for, for the home loan.
Choosing a good lender to guide you is the first step, along with a Realtor. I can give you contact info for excellent loan officers if you like. Just contact me.
You are headed in the right direction. It will just take some guidance and a little more time.
Best of luck,