ref: http://www.okonite.com/engineering/nec-ampacity-tables.html
generally see the latest NEC (National Electrical Code) standard but from the tables with assumed temperatures, the rating for 14ga copper is 15 amps (120V).
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A #14 copper conductor with an insulation rating of 90 degrees C is rated at 15 amps.
A #14 copper conductor with an insulation rating of 90 degrees C is rated at 15 amps.
A #6 copper conductor with an insulation factor of 75 or 90 degrees C both have an amp rating of 65 amps. If the #6 conductor is connected to a breaker having a 90 degree C rating then the conductor can carry an amperage of 75 amps
Using AWG # 3/0 copper wire you will have a voltage drop of around 3.8% at 68 degrees Fahrenheit. This should be acceptable to your local inspector but you may want to call them and make sure.
Use 15 amp breaker with 14 gage wire or 20 amp breaker with 12 gage wire. Either way will work just fine.
Use 8 gauge wire.
I would run 1/0 gauge.