Functional programming boils down to one simple idea: do everything with functions. No other language can show you the power of functional programming as Scheme will. It has a small core and it's easy to learn and with minimal accidental complexity.
Haskell is another language you can pick. It has a great community and can help you see programming from a different angle. Keep in mind that Haskell can be a bit frustrating at first. You will be introduced to a lot new concepts and paradigms.
As Jan mentioned, if you want to do something meaningful and get real work done, pick Scala.