I own both the 60D and the 7D. Best two lenses for these bodies are the 17-55 f2.8 IS and the 70-200 f2.8L IS II. Of course, this all depends upon what you shoot. Of the three that you suggest, I highly recommend the 17-55 f2.8.
So, what if you move to FF? If you're considering such a move soon, then consider the 6D with the 24-105 f4. This is the "FF counterpart" to the 60D and 17-55 f2.8, only better -- better low light, better color, greater focal range.
(FWIW I recently added a 5D3 with the 24-105 to my kit. I don't regret having the 17-55 that can only be used on the crop bodies, it makes a good backup system to my 5D3 if I need it. It also makes a good system for my daughter and potential apprentice who's interest in photography is growing. More importantly, for the past year that I've owned the 17-55, I got images that would not have recorded with a slower lens.)
The 24-105 is often a great buy as a kit, anywhere from $200-300 less than buying it solo. Buy it now and you'll spend a few hundred extra in preparation for the move to FF.
So if you plan to use the 60D for a while, then get a lens that works well with the 60D, you'll get more use out of the 60D. The 24-105 is a good lens on the 60D/7D, if you don't need the wide end and always shoot in lots of light. But, the extra stop of the 17-55 is big asset. If you move to FF, you can sell the 17-55. Sure, you may lose some money in the process, but it should be a near wash compared to the higher cost of the 24-105 solo (assuming this is your lens of choice for FF).
Also, for price, consider the Canon refurbished store.