What I would give for a $5K grant!
I think that 10-20 launches is a little low for getting to nationals. 20-30 seems more reasonable for planning purposes to make nationals. On the motor choice, our team is a Cesaroni team, although we might have to change that if production doesn't ramp up in time post-fire. The other local team that does well swears by Aerotech single use. Whatever you do, make sure your motors are all the same date code, and especially do a few tuneup flights on the same date code motors you will use at finals if that isn't what you used to qualify. We've found noticeable differences in impulse between batches.
As mentioned above, if you do make nationals, there are a lot of travel costs. From where we are, the travel costs dwarf the other program costs. Figure $100/night for hotel rooms for 4 nights, maybe 3-4 kids/room depending on your students, plus lunch and dinner plus transportation. It adds up pretty quick, even if you drive rather than fly. If you fly, add in rental car(s) for your teams as well. You can fly with TARC rockets in carryon boxes if you don't want to entrust the rockets to either shipping gorillas or checked baggage apes. If you want to carry your motors, you obviously have to drive. You can also split the difference and send an adult with the rockets and motors in a car and send the kids by air.
One other thing to keep in mind is that if you make it to nationals, the students need to be able to do EVERYTHING without any adult oversight, from building the motor to packing the rocket to reading the altimeter. You'll drop them off at the table where they get their eggs, and then wave goodbye until they are on the way to the pads. Depending on your students, that may play into your motor choice as well.
I hope this helps, even though I don't have very many hard numbers. Good luck on the grant!