Sounds like you're where you need to be for mortgage prequalification purposes. I recommend meeting with a Local Mortgage Banker to get prequalified for financing. The Mortgage Banker will review all facets of your loan request to answer your questions with regards to the types of loans and maximum loan amounts you could qualify for.
Congratulations on taking the first steps to purchasing a new home!
I would recommend just talking to a lender as there are a lot of other variables that play into the approval process. They will be able to look at all your information and give you all your options with no obligation. I could give you a name of a loan officer that is very patient and works well with first time home buyers. Feel free to contact me if you want her contact information. I would be more than happy to assist you in your home buying process as well.
Best of luck!
RE/MAX Advanced REALTORS
You are correct, there is more to it, but FHA would certainly be an option and even a conventional loan may not be out of the question. Your down payment, job time, credit details beyond your score and assets will also come into play.
I would encourage you to speak directly to a mortgage broker to find out your options and either start the purchase process or to take a few steps to improve your credit score. Best of luck.