I'd start with strings of integers, possibly the primes, or the Fibonacci Sequence.
If they're advanced enough that they can develop civilization that we can communicate with, I imagine they must have at least some mathematical knowledge, and sending them number-theoretic information would be a good way to let them know that we are 1) intelligent and 2) that we have reached a certain level of intellectual advancement. I would say that, of all things, it's probably the most likely common language we'd have.
I think a good starting point would be to send, say, the first 100 primes, and see if they send us back the next ones. If we could get communication going in this way, alternately adding numbers to mathematically defined sequence, we've already managed to get communication, and cooperation, which would be a pretty great, as far as first contacts go.
After that, it all becomes more nebulous. Possibly more complicated sequences? By learning what kind of mathematics they do, we might be able to glean something about their psychology.
Blessings
~ND