Lisp's biggest problem is that there's no overriding standard everyone sticks to. You don't just have to pick between Common Lisp and Scheme; you have to pick between several incompatible implementations of Common Lisp and several incompatible implementations of Scheme, as well as other little things like Arc and Clojure.
I would recommend starting with MzScheme. It's popular, it's actively developed, it has many libraries offering the features of a modern programming environment, and Scheme is somewhat simpler (not to say better, just simpler) than Common Lisp.