The differences between Common Lisp and Scheme are overestimated. They are, and some of them are important, but for real work you will not have problems with learning one and then the other. When I usually wrote both, I could switch between them without any problems.
If you plan to start with SICP, I would start to study the Scheme. If you plan to start with your project and decide that you need Common Lisp for it, I would start learning Common Lisp. After that, learning the second dialect is very simple.
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