A simple steadycam like support will work but you have to understand how it works before you buy one or make one.
The full blown steadcam has a camera support, some spring loaded four bar linkage and a support vest. The four bar linkage connects the camera support to the body harness while allowing the operator to move the camera any way they want. The idea is this; if you can walk with a glass of water in your hand without shaking and spilling it, you have the basic skill to start using a steadycam, because that's really what you're doing with the camera; you're walking without shaking it. I'll get to the stuff you need to know but first a little more on the 'real' steadycam. The reason for the spring loaded four bar linkage connecting the camera support to the support vest is simply to transfer the weight of the camera to the operator's torso so that it becomes nearly weightless in his hand. Remember, the steadycam originated when heavy film cameras were being used. A camera operator could not possibly hold the camera in their hand and walk with it. So, the steadycam essentially makes the camera weightless in the operator's hand, but there's more; Inertia. The heavy film camera has inertia. That is to say, even though it is balanced and weightless when attached to the steadycam and operator, it still has inertia because of it's mass. This means that the operator can not easily make it shake or tilt. It will naturally move smoothly. The more inertia, the smoother the camera will naturally move. That's why you can run up stairs or jump over tree branches and the footage will be as smooth as if the camera was floating on air.
The camera you will be using probably weighs about a pound. You don't need a steadcam to support it's weight. You could easily hold the camera and run with it, but what would you get? a bunch of shaky footage, and that's not what you want. So, if you attach your light weight camera to a support like this one;
You can get some smooth footage. Here's a tip; the heavier the camera and support, the smoother the video will be. You should add weight to the camera , which means you have to add more weight to the counter balance at the bottom of the rig. If you can get the fully loaded rig to weigh around 8 pounds, I think with a little practice you will be able to get some pretty smooth footage for around $50.