You should be safe in using 12 gauge wire, but upgrading to 10 gauge won't hurt anything, but still use a 20 amp breaker. I'd hard wire the compressor with type MC cable rather than use a plug and socket, providing you intend to leave it in one place. You'll only need a 12/2 (or 10/2) cable, rather than 3 conductor, as the neutral is not normally used on a 230v motor.

A little info on HACR ratings and inverse time circuit breakers;

http://static.schneider-electric.us/docs/Circuit%20Protection/Molded%20Case%20Circuit%20Breakers/0600DB0102.pdf

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https://www.schneider-electric.us/documents/support/codes-and-standards/circuit-breaker-markings-iaei.pdf

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The 20 amp breaker should be fine. The problem most people have is with the lights dimming when the motor kicks in. That is caused by voltage drop, which is caused by too much amperage going through too small of a wire. 10 gauge wire can help this, but other factors may also effect this.

I picked up 10g wiring and a 30amp breaker. But I didn't read this info till just now. Multiple forums I read through mentioned using a 30 amp breaker for this unit which was why i went with a 30. The wiring from the power line is brand new to our also brand new 200 amp outdoor main panel and meter box. From the main panel there is also brand new underground wiring which runs about 14' to the 100 amp garage panel. The compressor will use about 20' of 10g on a dedicated circuit. The garage lights are 8.5w LED so I hope that helps with possible dimming.

So far no problems running 30 amp and 10/3 (no neutral wire like mentioned). I used the black and red wires and capped the white. The ground is also there on the switch. The biggest problem is trying to bend and route the 10/3 because of its thickness. Out of curiousity, if perhaps the neutral was to be used, would this be considered a split phase 120/240 that uses both voltages?