IMO the most important feature is user friendliness seeing as how it's your buddies and students who will film you. Theres nothing worse than slaying a run only to find out the damn thing wasn't recording; I have physically removed unessential buttons to prevent mishaps. IMO the second most important feature is size; my camcorder is small enough to live permanently in my coat pocket...being able to have it on me at all times has been the key to getting video often (absolutely essential for progress!!). You have to keep in mind that few will understand why you need video in the first place and no-one wants to wait for you while you get the camera or do 3 takes because of gear mishaps. Do everything you can not to make this chore.
You are filming for MA, not a ski movie (unless you are Harald or heluvaskier
). Minimum requirements: at least 10x zoom with OIS and at least 1080p 60fps. I use the Sony HDR-CX405 which fits all the criteria and is dirt cheap.