If it happens to me to choose Scheme I would be using SICP as a resource. Is it a bad thing to do?
No of course not, why should it be? If you take the time to re-read some chapters and do the exercises, it's great. And the Scheme implementation shouldn't be that important either, since the feature-set that SICP is quite small, even compared to the rNrs require.
And since Scheme is more Algol like, and tries to stay away from some of the characteristically "scary" lisp-features like dynamic scoping, macros, etc. Of course, if that's what you're most interested in, there's nothing wrong with starting with common lisp.