Here's the first thing I would say against the 135, although I'm sure it's a heckuva lens the problem with all-around/general purpose may be the lack of zoom, it's going to rely on you to be the right area to frame the shot, so although you can zoom with your feet, you may miss a good moment being too close or far away. A good zoom in the same range would be the 24-105 F/4L, I've heard the 24-70 is amazing but it's more than twice expensive. Hope this helps, best of luck with your decision!
Ya I would look at the 24-105mm for an all-around lens. Anything with a wide zoom range will be all around. For a cheaper variant (aka more affordable) try looking at the 28-13mm, similar zoom range and more affordable. Of course the L lens is nice but it's not required because the 60D is a cropped sensor. Some food for thought and a cheaper alternative.