The later Type IIIs (like the Squareback mentioned above) used an analog electronic fuel injection system. The later Bugs (and Super Beetles) used a different version, also controlled by analog electronics.
I would recommend not using the original systems. They are quite primitive, all in all, and very difficult to tune and modify reasonably. I would consider something like SDS (
Simple Digital Systems EM-4) or one of the Megasquirt variants. The latter requires you to learn a lot about how injection works and do your own fabrication and such.
The single-carb setup is less than optimal as well, I think. The long-ish intake runners tend to promote manifold wetting; the heat risers from the exhaust combat that but take a little while before they get warm enough. I might consider a pair of little tiny single-throat carbs instead, but I'm not a carb guy.
The need for getting cooling air into and out of the engine bay (into the top, out the bottom) will make for extra aerodynamic challenges.
-soD