I'm sure you can get something for less than $500 that'll do the job. You pretty much don't have a choice anymore as almost everything is either harddrive or flash-drive based now. Tape-based cams are pretty much gone.
But that isn't a bad thing for you because you want something you can easily transfer and flash-drive cams are definitely easy to transfer.
What you really need to think about IMHO is how to get a good shot that really maximizes the quality of the video you're sending off to colleges ~ I think that will be much more important than the videocam you use to shoot the video.
I recommend getting a good mpeg editor to edit the video - check out Womble MPEG Editor - very easy to use and it doesn't re-encode the video.
And just to make it easy for the schools to which you'll be sending the video - I'd get a DVD authoring program that's easy to use so that when the school receives the DVD - they can just pop it in the player and check it out - and not have to figure out if it can only be played on the computer...what program you need to view the video file, etc. I recommend TMPGenc DVD Author for an authoring program.