What gauge of electric wire would I need for a 300' run?

A space heater is a big load, so is an a/c. 10 guage starting at 120vac over 300 feet will deliver 110vac at the other end at 15 amps. [7.7% drop] Two wire is unacceptable anyway. You need a ground. Don't be dumb and cheap and hurt someone. That's a long wire run.

http://www.powerstream.com/Wire_Size.htm there is a calculator here. 12 guage would deliver only about 106v. That's too low.

Neither will be good for two reasons, you need a ground wire for safety, and you need 10 gauge wire to prevent voltage drop at that distance, especially with an air conditioner. Go with 10/3, and if exposed to the sunlight for a long time, you need to get it with a sunlight resistant outer jacket.

Size does matter, and bigger is better, especially with electricity.

Get 10/2 with ground UF if your going to bury it . Underground Feed 10/3 with ground if you want 220volts

either will be fine / id go w/ the 12/2