I have the 17-55mm, and it's an excellent lens. But, f/2.8 indoors with ambient home lighting usually means ISO 3200 or even higher. While ISO 3200 is fine on my 5DII, I prefer not to go that high on my 7D.
Definitely get a 430EX II if you don't have an external flash - you can bounce that off the ceiling for nice lighting.
As for lenses, I'd consider a fast prime. The new 24/28 primes aren't fast, I'd absolutely take the 17-55mm over either of those. The 24mm f/1.4L II would be ideal, but it's expensive. You might consider the Sigma 30mm f/1.4, but since the 60D lacks AF Microadjustment, I'd recommend buying the Sigma (or any fast prime) from somewhere you can easily return it, and test the AF performance right when you get the lens.