Shutter speed is most important but nearly all will have 1/1000 or shorter which is all that's needed. The key is that the camera must have either a mode that makes shutter speed the priority (often called 'sports' mode) or a manual mode that lets you control it (rare except in professional video cameras or 'specialist' cameras). Don't expect to often have use of the fastest shutter speed because that requires a LOT of light unless you have a manual camera.
regular video will give you 25 - 30 FPS (depending on the video system where you live). More frames per second is nice but for the full swing 30 will give you a LOT of feedback. 'Specialist' cameras like the Casio that McIrishman uses can give you MANY more frames per second but these are not the best for recording family video (partly because they are shaped like 35mm SLRs vs video cameras).
If your primary interest is golf then I'd get a Casio (and I did