I agree with the others about asking for donations (doesn't need to be vintage -- you'd be surprised what people will give away for a good cause!). Other option might be to see if a local trade school or factory might be willing to donate or sell their used machines on the cheap.
I'm sure the $100 machines would work fine to start with, the issue will be how well they'll work after sitting in a closet for 10 months for a couple years and then taking the standard abuse that new sewers put their machines through. If you have a volunteer who can tune/repair machines, the $100 machines might be okay. Unfortunately, though, I agree with the others that cheapy plastic machines are easily broken (not that I broke a machine a brand new low-end machine in my first sewing class or anything like that
).