When buying a DSLR video camera you have a choice between Full Frame sensors or APS-C (cropped) sensors. A full frame sensor records the entire image that's taken into the camera through the lens. An APS-C sensor only records a cropped section of what's actually being seen by the lens.
Here's a photo that demonstrates Full Frame vs APS-C:
As you can see there is a big difference. What this means is that a 35mm lens on a camera with a full frame sensor is recorded as a 35mm lens. A 35mm lens on a camera with a APS-C sensor will record only a portion of the image making the 35mm lens appear more like a 50mm lens.
Wider lenses work best with any type of stabilizer so having a 35mm lens actually work as a 35mm lens can be very important. If you've every used a video camera with a long lens or zoomed in and tried to keep the video steady then you already know that the longer the lens is the tougher it is.
This doesn't mean you can't use a camera with the APS-C sensor on a steadycam and not get steady results. I use a Canon 7D and Canon t3i (both have APS-C sensors) with my SteadiGO, SteadiBRO and SteadyDSLR and get beautifully smooth results. Since my cameras have cropped sensors I use lenses from 24mm to 10mm when using a handheld stabilizer.
What you should consider if using an APS-C sensor is that if you want the equivalent of a 35mm lens you would need to use a wider lens closer to 20mm since it will be cropped by the sensor.
