I'd shot it over a black background, then composite it using transparency. They've done something similar back in the early 80's with Raiders of the Lost Ark: shot a woman in a pool and then used the composite over the footage, so it was looking like a ghost with the clothes floating.
Black background with good lighting to separate the character from the background.
As for moving, use a standard dolly platform and push your actor in front of the background. That's how I would do it.