In my opinion prime (non-zoom) lenses seem to be sharper and cleaner than most zooms. Of course that doesn't mean you can't break the bank and invest in a high quality zoom like the Canon EF 8-15mm or Nikon Nikkor AF-S 17-35mm.
Wide angle lenses help to smooth out video when using a handheld stabilizer. Also lightweight lenses are better on a handheld rig because it lessons user fatigue. An extra couple pounds might not seem like much at first but if you're shooting a scene multiple times or running around a live event you'll really start to notice any extra weight on the stabilizer. Here's a demo using a wide angle lens and a SteadiGO handheld video camera stabilizer.
Written by Aaron Marinel
Owner - SteadiRigs LLC