There are now many different types of video cameras that allow for the use of interchangeable lenses.
Finally camera manufacturers have run with the idea of SLR glass options for use in a digital format. Now digital filmmakers have a ton of choices when it comes to selecting the right lens for the desired look.
When it comes to what type of lens to use on a steadycam/video camera stabilizer there are some basic points to consider...
#1 - Focal Length
Basically what this means is the distance between the lens and the image sensor in the camera when the subject is in focus, usually shown in millimeters. Another way to think about it is your zoom options from wide to telephoto.
#2 - APERTURE
The Aperture of a lens is measured by how much light it can let in through its diaphragm. For example a lens with an aperture of f/1.8 is considered a fast lens where an aperture of f/11 is considered slow because it let's in less light.
A fast lens (larger aperture lens) is important for shooting in low light conditions, such as indoors and also for creating that beautiful cinematic bokeh look.
Bokeh is the blur produced in the out of focus area of a photo. This separates the subject from the background and helps to draw the audience to what you want them to see.
#3 - IMAGE STABILIZATION / ELECTRONIC IMAGE STABILIZATION
There are a lot of lenses that have built in image stabilization. This doesn't mean it gives the look of a steadycam but it does help reduce that handheld, motion sickness look.
A prime example is the film "The Blair Witch Project". I watched it in the movie theatre (many years ago) and it was the first movie to ever make me nauseous. This actually happened to a lot of viewers and it was because of the handheld, frantic filming. This is the effect that built in image stabilization reduces.
So the simple answer is WIDER ANGLE LENSES (10mm - 35mm) WILL APPEAR SMOOTHER on a camera stabilizer, handheld steadycam, dolly, crane, slider or jib. Built in image stabilization will help but isn't curtail with a wide angle lens and maximum aperture is always a consideration as with any lens.
Currently my primary lens for use on my SteadiGO glide-cam is a Samyang 14mm f/2.8. It's a 100% manual lens which I like (coming from a film background) and it's also great practice for when you need to use any lens in manual mode.
Another nice thing about a wide/manual lens is focusing. Because the lens is wide you can set the focus for most shooting and keep almost everything in focus. This is also not a fisheye lens, something you should look into carefully before buying a wide angle lens, otherwise you might end up with a distorted bubbled look.