You definately want to upgrade from the kit lens - at the moment you're carrying around a vastly overpriced and heavy digital compact.
I have the Sigma 18-50mm F2.8 EX DC, a lens with which I am very happy. It's sharp as a tack and lets in a lot of light, which is important for climbing photos. Not too expensive either, as these things go. Autofocus is slow and noisy compared to the canon lenses though.
The essential lens is the Canon 50mm F1.8: it's small, it's light, it's fast and sharp and it's a great focal length for climbing shots. More importantly it's cheap.
You won't need both of the above though, so choose between keeping the kit lens, and using the 50mm if you want qualiteee, or shelling out for the sigma.
p.s I also have a Sigma 18-50mm F3.5-5.6 DC kicking around. Quality wise it's between your kit lens and the lenses above. Not shit, not great. But it's yours for 40 notes if you want it.