300-400. Every NROTC/NJROTC unit in the US is authorized to nominate three candidates. For extremely competitive candidates (those who might be in line for an LOA), an appointment might be offered early on with only a NROTC, but highly unlikely. Don't count on it. The vast majority of all appointments are offered in the spring only after the application deadline and the Academy is able to rank ALL candidates and ascertain exactly who they want. Then they begin to match these desirable candidates to available nominations. As the catalog states (again), help them out. Pursue all sources available.
As far as gaining an appointment, this avenue is truly a needle in a hay stack. However, as an avenue for your ROTC instructor, who probably knows a lot about you, to write a 'glowing' endorsement, the nomination is invaluable.