Agreeing with Bump.
I do use the 17-55mm f/2.8, it is a *friggin' fantastic* lens. Yes, it is an upgrade of the kit lens. It is a true wide-angle to moderate telephoto. For video use, that means it goes as wide as you want without significant wide-angle distortion, and can pick up a head & shoulders shot at a reasonable shooting distance.
I was turned on to the Tokina 11-16mm f/2.8 by a pro video shooter, it's a great ultra-wide-angle, meaning that you accept some distortion for the very nice view. Wider than that goes to something like a manual Rokinon/Samyang 8mm semi-fisheye.
In my experience, 55 is just barely long enough for picking up people at reasonable working distances. Many times I've wished for something longer to pick up an extreme closeup (part of a face, for example). I bought a Sigma 50-150mm f/2.8 for that, *beautiful* lens, but it doesn't come out much.
Other factors: They're all f/2.8, 77mm filter size. Since you tend to lock down ISO & shutter speed for video, having a max aperture that doesn't change with focal length is valuable.
These are three very fine lenses for video. No IS on the Tokina... But the Canon & Sigma have it.
As of the 70D +, we're now getting to the point where autofocus (finally!) has some use for video. The combination of face detection, focus point tracking, and touchscreen selection actually works in practice. I hear face detection works better with STM, but... I do want to try the 18-135 STM, even though it's a slow lens with non-constant max iris.
I have access to a set of Zeiss primes for video. They're really only useful for cinematography-style shooting when you're in control of the set. The 17-55mm lives on the camera... Because it gets the most use!
From the upper left corner of the U.S.
Photos, Video & Pano r us.
College and workshop instructor in video and audio.
70D, Sigma 8mm, Tokina f2.8 11-16, Canon EF-S f2.8 17-55, Sigma f2.8 50-150 EX OS, Tamron 150-600VC. Gigapan Epic Pro, Nodal Ninja 5 & R10.