Best camcorder for short films?

I would recommend a Sony Handycam HDR-XR160, but I think that would be just outside your budget, but maybe you could get it on ebay or somewhere.

Otherwise, I would go for the Sony HDR-CX130

Panasonic also has a a similar one in your price-range: Panasonic HDC-SD60K
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I would get an external mic to feed in (buy a shot-gun microphone)—don’t rely on the built in mics. Another trick is to place a recording device closer to the person (I’ve even used my iphone on occasion.)
To be honest, I think as long as you are shooting in HD and the sound capture is good, the cutting edge should be on the quality of your content (script, acting, editing, creativity), rather than the quality of the camera. I know that’s what I would be looking for in an applicant’s work.

A lot of ‘snapshot’ digital cameras can take HD video these days… Start with that and look for the best lens that fits your budget. ..Although the mic on those is not so hot and most of them don’t accommodate an external mic.

Don’t DON’T buy a camcorder. Invest into a DSLR.
A Canon, Nikon, doesn’t matter. The combination of interchangeable lenses and a DSLR sensor has huge benefits for shooting professional style video. Honestly, nobody is using camcorders to shoot video anymore, and it seems like you’ll be studying film, so a DSLR is even more important then.