I think this is due to the fact that I learned to program in C. Nowadays I work mainly with python/ruby/javascript, but I got the feeling that I could improve myself as a programmer by learning Lisp.
Exercises includes sorting, search in binary trees etc etc
http://mitpress.mit.edu/sicp/ is almost the same but with more math/physic background (uses numerical oriented exercises very early). You'll have to write recursive subset, n-queens, matrix-composition functions.
Apart from Racket, Clojure is also a nice Lisp to get started with. It runs on the JVM.
I'd advice against learning Common Lisp as your first Lisp these days, even though Common Lisp is what On Lisp is about.
Similar, if someone asked about a modern scripting language, I'd send them away from Perl in favour of Python or Ruby.
If they goal was explicitly Perl (or Common Lisp) that would be a different thing, though.
why?
I don't find that at all, and a large reason for learning common lisp is as a learning exercise to become more intimately familiar with lambda calculus and s-expressions. The increased expressivity of clojure (for example) may hinder the very thought processes that make lisp a dialect worth learning. Of course they are both fine languages, but most people now advocate the learning of a LISP not for practicalities sake, but rather just to demonstrate real life things that those sets of languages do differently than nearly every other language, and to allow the programmer to take from those experiences and apply them to their language of choice.
From THAT standpoint, i'd advocate CL first, if not only for forcing the user of the language to experience the follies of certain practices, such as the namespace issues that Clojure tried to fix about CL.
Any Scheme implementation will be better for this. Much less primitives, one namespace for everything, hygienic macros, immutablity by default/encouraged.
CL is exactly the opposite of that - it's complicated because it wants to be practical. And for the most part it is. It supports procedural, functional and OO programming, probably logic programming too with the right library. It's designed as a real system for solving real problems - and as such is not the best tool for learning about lambda calculus. Actually you could program imperatively in CL for the long time before ever feeling awkward.
Scheme, with it's mandatory TCO and encouraged immutability is much better for learning lambda calculus... and about Lisp in general.
In many ways Common Lisp is still a much better language than Clojure or Racket. It isn't old, compared to pretty much anything from the 80's it has aged unbelievably well, and while it has some "stale" parts you can call ugly, I find many parts of clojure or racket much uglier. All in all, it is one of the best high level languages around.
(In case you ask: Common Lisp is a useful target, if you want to port programs from even older Lisps, like emacs' elisp.)
On the other hand CL has CLOS, an object system which puts others to shame. And reader macros to define your own syntax. See cl-annot to see the decorator syntax from python being ported to CL or how to give hashmaps Ruby syntax [1].
What's practical about a Lisp-2?