Most of the dispatchers I know came from checkin or other departments within a ground handling agent. These jobs give you a good background (most of the time) from which to base a career in dispatch...
A checkin agent will see some of the problems a dispatcher has to face (and help solve) and can learn quite a bit just from observation. Also, you may be able to 'shadow' a dispatcher, as long as you're polite and don't make a pain in the ar*e of yourself, which I have seen happen (twice) with over zealous wannabes who got a bad name for themselves.
Also coming from checkin will give you the opportunity to get to know many of the people you'll be working closely with in the future, regardless of the job you finish up in. I love the airport...