I'm sure you will love the 60D. It's a great camera. Lots of features and should be useful for a long time to come. It will be perfect for what you want to do now.
But....you've come to a rumors site! We enjoy gazing into crystal balls, reading tarot cards and tea leaves to foresee the arrival of newer cameras, and lenses. We can also foresee the future camera purchases that people will make.
If you're long term interests are in sports and wedding photography, and you're budget was marginally higher, I can see that you would be happier with a 7D or 5Dii. If you take up photography professionally (or at least semi-seriously), chances are that is the direction you will head in. Looking into my crystal ball, I can see that Canon will replace the 60D, 7D and 5Dii with some excellent new models this year. You will be kicking yourself that you didn't grab a run out deal on a 7D or 5Dii, or pick up one of the new ones.
Therefore, I'm going to echo some of the previous comments. Buy a cheaper body and buy some better lenses.
Better lenses will make taking great photos easier. Feature-wise, there isn't much difference between a t3i and a 60D. Image-wise, I believe that they are virtually identical. Then in a few year's time, once you've got a good understanding of where your interests lie, maybe consider a newer body that is more tailored to your needs (eg with more frames per second, better autofocus, less noise etc). You'll have some great lenses to use in the mean time. And if you decide to upgrade bodies, one of the real benefits of buying Canon is that there is a huge interest in second hand equipment. You won't lose too much on your old camera.