Hey Bob, cool Vette - the early C4 was the first giant step for Corvette becoming a world class sports car.
In general a flywheel is used with a manual transmission and has the machined surface for the clutch disc to mate with, a flexplate is used with an automatic transmission and has tabs welded on to mount the torque converter.
Since you have a high performance engine and expect to see high rpms to make 400HP with a 350, you should invest in an SFI spec flywheel or flexplate. The stock part may be adequate for street use, but any competition use would be risky (picture a half inch thick steel blade emerging from the floor board on it's way to exit the side of your car, then think about where your feet and legs are). While you have it apart be sure to service the front seal in the trans, pilot bearing in the engine, and if you have a clutch check/replace the clutch, pressure plate, and throwout bearing (I'm thinking that if your missing teeth, you've probably got clutch issues anyway).
As for transport, I would use a trailer, I know its not out of my pocket, but if the car isn't worth a trailer, why do all this work on it?