I know that the strength of the magnetic field and the speed by which the conductor passes the magnetic field have an effect on magnetic induction for the voltage output on a generator.

I also know that when conducting electricity from a source to and end user that the longer the distance the thicker the wire needs to be or else eddie currents and resistance will cause the wire to overheat (and thus either melt or cause a fire hazard.)

What I want to know is that when building my DIY generator, do I also need to adjust the wire size to the length of wire? Will using a thicker wire or thinner wire make an impact on efficiency of magnetic induction to produce electricity?

For example, if I want to be sure I have a greater voltage output or whatever (with less resistance or impedance,) do I increase the thickness of the wire or decrease the thickness of the wire?