the closest wire size calculator I can find (
Electrician Continuing Education) says to use 10awg - I said that the run was 500ft. 10awg should also supply you well if you put an outlet and ever want to plug in something big (fan, power tools, space heater etc...) - you know that you will
look for "outdoor" and "direct bury" ratings on things- they should last longer.
And know that you are indeed rednecking this, be careful as the years go on, keep your eye on the terminations etc...
Mike Holt Enterprises Home - real electricians hang out there, if you want some better advice
-John