Good questsion Jason, thankfully the government is back up and running (well, technically at least
) so the USDA site should be going full throttle soon.
Assuming you are in a qualified, lower density area, a USDA loan is a great choice with the 100% financing and is a great product for 1st time home buyers.
As Williow and Pfhtex attested, generally 640 is the score that most lenders will go with. Often times lenders also have outlets where they can broker the loan to a lower number.
In my professional opinion, you could get a second look at the application by another lender. A good lender will be able to formulate a plan to quickly boost your credit, I call it a rapid rescore. By doing this, the lender can formulate a way to get your girlfriend an efficient way to get up over the 640 mark (i.e. which credit card to pay off, something along those lines).
I would advise going against FHA, as your monthly payment is very likely going to be higher due to the higher mortgage insurance cost. Hope that helps!