Yes, you can pick up and play with the starter kit.
The starter set comes with everything you'll need to a game, technically. The three dragons that come in it; red, blue and copper are all you need to play but getting more figures later on doesn't hurt if you want to have large battles.
Ground works the same as air, save you can pivot on the ground and not in the air. Both use a movement dial that you use to select the distance to move a unit and in what direction.
I've ordered out for the starter kit and the first two waves of merchandise. 3 more waves are on the way, some big things from those are a Silver dragon, Dracolich and Drizzt.