Add another vote here for the 15
-85 IS USM.
furthermore, if you're only going video and not photography, save the money from the 60D and get a 600D (ie, 600d + 15-85 > 60d + 17-85). Actually, for a starter who won't do sports and birds, i'd recommend that for photography too.
Or also the 17-55 f2.8 is a bit more again, but that decision is pure 'extra light' vs 'extra length'.
If you need faster lenses for video you could also get some used M42 mount lenses. I got my 35mm + adapter for less than 20â‚¬ from ebay. I'm sure you can get a 35mm + 50mm + 85mm for about the price of a EF 50 1.8 II. They will have better build quality including better manual focus rings for video.
i'm also an MF-prime fan, especially M42. But not all of them are good, and the good ones aren't cheap. SMC Takumar are one of the best non-zeiss you can get, the 50mm f1.8 and f2 should be less than $50 shipped. But go up to the 50/1.4 and you're well over the price of a niftyfifty (which has AF).
on the fast wide end there's nothing cheap, 28/1.8 are dime-a-dozen from a heap of different companies, but watch out for the quality of some unkown-names.
faster than that: zeiss 35/2.4 flektogon go for $200 and up, and takumar 35/2, nikon 35/2 & 28/2, OM 35/2, MIR 24N&M 35/2 all go for upwards of $100-150. (trust me, i search on ebay every week for something cheap in this range). still cheaper than the ef 35/2 and better IQ than a fast sigma prime though.
85 f2 look for a Jupiter9 soviet built, again lucky to get one under $100, otherwise spring for the EF 85/1.8 (or a mamiya 645 80 f1.9 MF for maybe the same price).
i suppose it depends what you call 'fast', if you expand it to f/2.8, then you can get a lot more range and a lot cheaper. but i'd spring for the 18-55 f/2.8 and not bother with the primes in that case...
also, forgot to say, and i don't think anyone's mentioned yet, if you're interested in video: Microphone.
even if it's an old crappy thing, just the act of getting the microphone away from the body will get rid of any AF motor or IS sounds, external mics can have a wind-sock put on too. Doesn't have to be a classy Hot-shoe Rode or Sennheiser, although they are better. Try pick up and old sm58 from a music hire-shop, they take beatings for years and live to tell about it. (kinda depends what you're filming though, more directional is probably more versatile)