If all you need is
slow-motion "normal life", stuff, you *might* be happy with merely capturing NTSC standard 30 fps video and using the video editor to slow things down to no more than about 15 fps. Lower than this and the video gets a bit "jumpy" moving frame to frame. Perhaps you can try this first with essentially any normal speed video to see if it will slow to the level you need.
If you need to either slow things down a lot more or are expecting to have very high quality and high-speed activities recorded and slowed (like an arrow or bullet shot or high speed manufacturing process, etc.) then use of a "high speed camera" rather that a camcorder would be appropriate.
In any case, if the lighting is "good enough" (nice, bright, full spectrum sunlight) video recording devices (like the GoPro Hero series) that have high speed video capture (240 fps) capabilities can do a fine job. In the price range you state, you are in the "prosumer" camcorder area. Generally, these camcorders are not designed for high speed video capture/slow motion playback. If you are thinking quality similar to the slow motion (~1,500 frames per second) video playback televised during the World Series, check into Vision Research and their Phantom line of high speed cameras. NAC, Photron and Fastec and a few others make high speed cameras that can do what you want. MythBusters and Time Warp use them for their high speed sequences. Your stated budget is about 1/8 their entry level prices unless you can find a used one in good shape.
We don't know what you plan to use for editing, if slow motion is all you need, what sort of video you need to be slowed and how slow you need it. We also do not know what computer you are using, which operating system, which editor - so we don't know if your editing platform can deal with various video formats...
Would you like to keep discussing this here?