If using a generator, an ammeter is the correct choice for monitoring charging system operation and a #10 wire will be adequate. If you're using an alternator, it may not give you a true picture and the wire needs to be sized to the maximum possible continuous load when driving. A voltmeter will be a far better choice. This is because generators and alternators don't produce their power outputs in the same way even though they operate on the same basic principle.
That fully depends on the draw by the amp, I have built systems using 175 watt amps and 8 gage wire and 2500 watt systems using 0/2 gage wire
Go with what Crazy Steve suggested in post 3. He is a legit wiring guru on old hot rods. Still, a generator or alternator is only going to put out the amps that the battery or system asks for. That comes down to how many amps the starter used cranking the engine to start it, how many amps the head and taillights draw, A bare bones hot rod with a good battery, plain old headlights that aren't halogen and no accessories doesn't draw many amps after the generator or alternator puts back what was drawn out of the battery at start up. What ever you add electrically that will put a draw on the system raises the amp flow through the ammeter. Aff Scot079's 175 watt Amplifier and your draw increases immensley and you have more draw than an ammeter = AMP meter can handle. Personally I vote for the volt meter unless nothing except an ammeter will do.
Aren’t there a couple types of Amp meters ? Maybe a shunt type with just the loop with wire running through the loop would be best . Best for me and safe operations is volt meter by 100x .