You can sign up before school or after residency. Different states have different awards. Iowa for instance will pay back full tuition but Missouri (sorry, I'm a midwestern gal) will only pay up to $25000 a year. Usually they are a year for year basis. The ones that I've heard of include FP, EM, Peds, IM, or mixtures of the above as primary care. You have to serve in an underserved county, but not necessarily in a tiny town or out in the country. Kansas considers all but four of it's counties as underserved.
I don't think there is a lot of competition. Theres such a great need they will take nearly whoever, although if you want to sign up before school starts, its better if you sign up for the state you reside in. (or have close ties to).
Take my information with a grain of salt, I am also premed. I've signed up with the Kansas medical student loan, which will pay my tuition and a monthly stipend. I'm really excited about it.