As many before me have mentioned, I would decide on what camera you're going to buy before choosing lenses. The obvious influence it will have on your lens choices will be the camera's lens mount (EF, MFT, etc.)
I shoot on the 5D Mark III and primarily use zoom lenses like the 24-105 F4 L IS for video these days. It all depends on what you're going to be shooting. I work on a lot of corporate jobs and the like where the shooting is run and gun and I don't have time to balance a steadicam or even think about laying some track. Therefore, the Image Stabilisation from the 24-105 works in tandem with my shoulder mount to get nice, floaty coverage. It also saves me running around like a headless chicken to get wides followed by close ups - I just zoom.
If, however, you're shooting films or are in a studio a lot and have the time to swap out lenses and change the lighting, then primes are much more the way to go.