The question is irrelevant if you don't include the amperage.
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The key parameter in sizing wire is the current requirement. Once you know that you can look up value in a wire gauge table. The length of the run is important for longer runs because of the resistance of the wire itself. Aluminum wire requires a larger diameter than copper for the same current. Once you calculate the wire size you can then size the conduit.
You size wire by the current. Various insulations are rated for voltage, temperature and the medium where the wire will be run.
Depends on the size of the circuit which you did not list.
Presuming that you would like the least expensive installation, the following is calculated on overhead aluminum wire. The wire size needed to hold the voltage drop to 3% would be 3/0 MCM. If the installation could be run on 240 volts then the wire size can be reduced to #2.