As you didn't mention any restrictions besides your subjective interests and emphasize 'rewarding to learn' (well, ok, I'll ignore the static typing restriction), I would suggest to learn a few languages of different paradigms, and preferably ones which are 'exemplary' for each of them.
- A Lisp dialect for the code-as-data/homoiconicity thing and because they are good, if not the best, examples of dynamic (more or less strict) functional programming languages
- Prolog as the predominant logic programming language
- Smalltalk as the one true OOP language (also interesting because of its usually extremely image-centric approach)
- maybe Erlang or Clojure if you are interested in languages forged for concurrent/parallel/distributed programming
- Forth for stack oriented programming
- (Haskell for strict functional statically typed lazy programming)
Especially Lisps (CL not as much as Scheme) and Prolog (and Haskell) embrace recursion.
Although I am not a guru in any of these languages, I did spend some time with each of them, except Erlang and Forth, and they all gave me eye-opening and interesting learning experiences, as each one approaches problem solving from a different angle.
So, though it may seem as if I ignored the part about your having no time to try a few languages, I rather think that time spent with any of these will not be wasted, and you should have a look at all of them.