Out of the three, Warlock is the easiest to level. Your mounts won't cost you much compared to other classes too. Beware of the rogues though, you'll probably be low health most of the time while leveling and if you're playing ally side, the undead will just clear your fear. We all know vanilla wow is 89% undead rogues.
You could also give Shaman a try, it seems to fit your criteria. It's mobile, you can either melee dps or long range dps, you can heal, the leveling is easy and you get a 30% movement speed form at 20.
