One thing that helped me when I first got started: I bought a 50mm f/1.4 and just stuck with that on my Rebel for a long time. It helped me really get a handle on composition and forced me to recompose with my feet, instead of just zooming in/out. I believe I became a better photographer because of it. You can get a Canon 50mm f/1.8 for like $130, probably the best lens anywhere for the money. After that, you can start deciding how to add to your stable.
I agree with that. At the beginning of your photography career you have the most potential to develop your photography talents the fastest.
As a past photography instructor I have seen that zooms tend to kill any photographic intuition that would be normally developed by a new photographer with a prime lens.
With a zoom lens you can just sit there not being a good photographer and you'll never even know it. And keep getting mundane shots.
The over-arching thing about photography isn't cropping, composition, etc.--it is first of all what is in the picture and second of all from what perspective you are taking the picture from. In other words, where you physically are, in a relationship with where the subject physically is.
Once someone becomes an expert with lighting, their equipment, and all of that, photography basically boils down to the relationship between the subject and the camera, which is acting in the place of eyes for whoever will be viewing the photograph forever after.
A prime lens teaches you how to have this relationship between the camera and the subject, whatever that might be. A zoom lens does not teach this. It makes you think about zooming in or out, or getting around obstacles, rather than a simple relationship with the subject.
A zoom is like someone who stands in one place and screams for what they want at whatever volume is needed to irritate everyone into paying attention, rather than talking in the right tone of voice for each situation that is at hand.
As soon as so many people stopped using zoom lenses, for me I have seen for them the true world of photography open up and blossom.
The 50mm f/1.4 mentioned is an excellent choice, and I would highly recommend the superb f/2.8L 200mm lens at the ridiculously cheap price of about $800 as your next lens (it will revolutionize your photography, and it is equivalent and just as good as the 300mm f/2.8 $11,000 lens on your 60D camera). You can keep your kit lens for any wider angle shots that you need.
How far will these two lenses put you ahead of anyone else? Light years.
A lot of people think that they want a lens like a 28-300mm.
At 50mm and beyond you would be shooting closer to f/5.6 than f/4.
The 50mm lens is sharper and lets in one, two, three, four stops more light (f/5.6, f/4.0, f/2.8, f/2.0, f/1.4).
This is SIXTEEN TIMES more powerful of a tool for your photography than the zoom lens.
And even if that were not true, prime lenses are still better for learning and executing the art of photography and the relationship with the subject which is all important as soon as all the technical details are mastered.