I woudn't run a 10-2 . I'd suggest running a 10-3 or larger, depending on what else you want to run out there. That wire would be connected to a sub panel which would hold several breakers. You could hard wire the compressor to one of the breakers. What about lights, receptacles? Do you need those too?

Is there room in your main panel?
Sounds like you need to find someone who knows alot more about electricity to do the work.