I wouldn't mess with the 35/2 but there are folks here that like it. Personally I find it's too expensive for what it offers. You'll find a lot of threads here from folks asking about alternatives like the 30mm sigma. There are a lot of other EF-mount 35mm lenses around as well. Ever since APS-C cameras showed up folks have been looking at that 35 f/2 & wondering if/when Canon will deliver a proper modern "standard" focal length lens for APS-C. The closest they've come so far is probably the new 40mm f/2.8 STM pancake
I'd say your choice should be between the 50 f/1.8 and the 40mm f/2.8 STM pancake. If you shoot a lot of video then the STM may be worth the extra hundred bucks for you vs. the 50 (though I don't know if the 60D can take advantage of the STM). It's certainly better built & the AF is better, plus it's smaller. Apparently it's amazingly sharp
But don't knock the little 50. It's extremely light, decently sharp when stopped down a bit, and cheap as chips
Another extremely fine lens that won't break the bank is the 85mm f/1.8 USM
. The AF speed is in the same ballpark as my 135L and the IQ is pretty close to L territory from f/2.8 and on. Think of it as a "baby L" & you get the picture. Basically every Canon telephoto prime from 85mm on up pretty much rocks, which is why a lot of us are here in the first place :-).
If you've got the cash, I'd say get the 40 (wider, sharper) or 50 (cheaper, more luminous) AND the 85. Maybe take one now & save up for the other.
Good luck :-).