The micro 4:3 cameras from Panasonic and Olympus can take as good video as most video cameras we have seen. Some Recent models also take 4K video. Some of the cameras can be found for under $400.
While the video itself is usually great on these (and DSLRs, for that matter), the audio pickups, focusing, and zooming leaves much to be desired compared to a dedicated video camera, which will usually have a larger shotgun microphone, parfocal lenses, and AF optimized for use with video. m4/3 and DSLR video are really for the realm of external audio capture and manual focusing, even today.
I've been out of the market for a while, but Canon, Sony, and Panasonic have really good video cameras. Do expect to get a second battery and extra media, so try to keep it at $300 or less for the camera itself so you have room in your budget for the battery and cards. If you have a local
Best Buy or similar store, you can go in and try some out before you buy them - most within a particular manufacturer will handle about the same way, so once you have an idea for that you can order online intelligently. Nowadays, with 1080p being commonplace on $200 models, and BSI CMOS sensors being de rigor, it's pretty hard to go wrong.
One tradeoff you'll have to make is in sensor size versus zoom range - the larger the sensor, the shorter the zoom range tends to be, but the better the camera is in low light. The cheapest camcorders have 1/5.6" sensors, but better ones have 1/2.6" or 1/2.3", with 1" being the biggest you'll usually find before you get to interchangeable lenses. For me, I'd trade to a larger sensor any day of the week over a zoom lens that's beyond what's usable easily.
