I think you have the right idea to start in the 250 class. I started out in the superstreet program and after graduating to a novice license I chose the 250 class because it is a cheaper platform to purchase and race. It also forces you to work on techniques at a more moderate pace that might feel rushed at the pace on board a 600cc+ bike.
Yes weight will be a disadvantage but as a starting place you should still enjoy it a LOT!
-2cents