First of all, welcome!
Two and a half years ago, I was in the same exact position you were, just starting out with a DSLR, frustrated with the awful, red-eye-laden shots my P&S was taking in indoor, low-light situations. There was definitely a learning curve once I did get my DSLR (I started out with a Rebel T2i)- my initial shots weren't much better than my P&S shots, kept getting blurry/OOF shots and wasn't really sure why it was happening. Long story short, to take full advantage of the new features and additional control I now had, I had to read up all on the basics of photography, talk to people, and practice- learn through trial and error. You'll find out that things as small as the way you hold the camera, your stance, etc. can affect the quality of pictures you get. Until good technique is achieved, it really doesn't matter what lens you start out with- the photos will likely look the same.
What I did was I got my T2i/kit lens combo, used that to get comfortable with the camera, learn it, etc. As soon as I was ready to do some serious work with it though, I immediately ditched the kit lens and went for something better (the 24-105 f4). You can go ahead and start out with the 60D and 18-135 if you want- but I think you'll find that as you improve, you'll want a better quality lens. The T3i/60D/7D/5DIII are truly high-megapixel beasts that demand high-quality lenses if you ever want to see their full potential. If you want to jump right in, you might want to think about a cheaper body (a Rebel series) and use the money saved to get something like the 15-85mm lens (praised highly by many people here). When it comes to picture quality, the lens is really what's most important. You'll get higher quality shots with a Rebel and a 15-85 or 50mm than you would with a 60D or 7D with 18-135 or 18-200.
Kind of long, but hope this helps.