For your purposes, an older cheap analog model might be acceptable. Analog models are going the way of VHS and audio cassette tapes. But if it will do, then you can save some scratch.
But, assuming that you want to also use it for general "family" use, go for digital tape. The straight-to-DVD models also work, but are not a good idea if you intend to edit and mix the video on your computer. Otherwise, they are OK.
Optical zoom is where it is at. Digital zoom throws away image quality. To me, any digital zoom over 2X or 3X is worthless, as the picture quality becomes much worse.
For a complicated mechanical device like a camcorder, getting an "extended warranty" is probably not a bad idea.
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Darwin was wrong -- I'm still alive