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Beginning with Common Lisp should be more rewarding. There are also vastly superior learning resources for anyone looking to learn the language.
Peter Seibel's Practical Common Lisp is a fantastic (and free) book: http://www.gigamonkeys.com/book/
[The Author] devotes more than a third of the book to developing nontrivial software -a statistical spam filter, a library for parsing binary files, and a server for streaming MP3s over a network complete with an online MP3 database and Web interface.
But don't use Lispbox as recommended in the book. Portacle <https://portacle.github.io/> is a newer and better alternative. It's basically a portable Common Lisp development environment with everything you need to start hacking Lisp right away.
Resources to learn Scheme used to be scarce and unsorted. Maybe the situation's a bit better now that Guile is gaining some attraction?
I half expect someone to spout the "Read SICP" meme. It's still a good advice, if you want to learn the hard way.