I bought one last year for the same purpose and used it to tape most of my races last year.
See this link for example:
Subdriver in car Video, Lap 1 2003 SCCA Valvoline Runoffs
Lots of video cameras fit your needs.
I bought a Sony Mini DV DCR-TRV38 for the following reasons:
- Image Stabilization mode (which I always use)
- Widescreen mode (my TV is 57" HDTV)
- Integrated 1 Megapixel digital camera (I didn't have digital camera and wanted something to snap quick pix of work on the car)
- Fairly small and light
For a mount, I bought the I/O port camera mount. It bolted right to my roll cage and worked great all year.
