I, too, would love to become a runner. Actually, one of my recurring dreams is where I'm running long distances and actually enjoying it and it feels easy. This must be my mind and body telling me something!
I think you definitely want to build up your distances slow. When I've run in the past, I've increased my distance too quickly and it just felt too difficult. Then I'd get discouraged at how hard it was and find reasons not to go. Building slowly and steadily will make it manageable and tough, but not TOO tough.
Good luck!
Ann