The OP specifically says needs to invest in a camcorder (not DSLR). Not that there's much difference these days. No mention of needing this or that like shallow DOF or wide FOV. For that cash, pick up a decent mic, a H4n, and a TM700 and still something left for rigging and cables and stuff.
I've actually got more invested in LED lights, *pods, and stuff than I do in my camcorder at the moment. Although I do intend to upgrade my camcorder SOMEDAY. But I've also got more invested in just Audio, than the OP listed for the whole kit.
Besides MOST camcorders currently out there are little more than glorified 720p camcorders anyway. They might save in a 1920x1080 pixel format, but their image is derived from say 900x800 pixels. And that's probably one of the good ones.
Was there even mention of needing HD? If it's anything like the college I went to, the curriculum was devised long ago and the tech never upgraded. People were being taught to splice tape and stuff at my college in the MID-90's. As in this is what you'll do (and get paid) scenario??? Chances are that the school is still in SD mode IMO. Although if you want to exploit your peers with your pretty toys, you'll definitely want HD. Music majors are often required to have their major things recorded, and to pay the recorder. And the theater department and other things which could help fund your pursuits without having to do other more menial work.