If you're going to be using your DSLR primarily for video, you have many cheaper options for lenses.
Still photography utilizes the full resolution of your camera's sensor, so a sharp lens will go a long way. When you shoot video, each frame is a much lower resolution than a regular still photo from your camera. For the Canon EOS 60D, a still frame has a resolution of 5184x3456, which is roughly 18 million pixels. Full HD video has a resolution of 1920x1080 which is just over 2 million pixels. The sharpness of your lens when taking video is not nearly as important.
Something you'll want to look for is maximum aperture. Depending on what type of videos you make, you can do most of your work with a maximum aperture of f/4.0, but a larger one like f/2.8 will obviously give you more options and flexibility.
Another thing to look for is a constant maximum aperture. If you plan on zooming during shots and your lens has a variable maximum aperture, you'll notice the shot get visibly darker throughout the zoom. For example, my Canon EF-S 17-85mm f/4.0-f5.6 lens changes the aperture as I zoom from 17mm to 85mm.
If you're considering buying a third-party lens, you should also consider whether or not you want autofocus in movie mode. If you decide to use it, skip this paragraph; you won't like what you read. Otherwise, you might consider purchasing a third-party lens that only has manual focus. If you think about it, autofocus is really nice for still photos, but not necessary for video.
That being said, I'd look into the Tokina 11mm-16mm f/2.8 lens for wide-angle shots. It's about $700 on Amazon right now. It doesn't have AF nor does it have image stabilization, but it's $250 cheaper than Canon's 10mm-22mm lens and has a larger (also fixed) aperture. I know that the guys at Warialasky use this lens in many of their videos.
The Canon 17-85mm f/4.0-5.6 is also a good option since it covers a wide range of focal lengths, has a reasonable maximum aperture, and has image stabilization. Also, it's fairly reasonably priced at $569 new. Just don't zoom during your shots since the maximum aperture isn't fixed.
Here's a video that gives some good insight for picking video lenses.