Pull up an ampacity chart for the type of wire you will be using. Select wire size that matches your desired amperage. This will be a starting point.
Next use an online voltage drop calculator to determine final size based on run length. You want the voltage drop percentage to be less than 3%. At 275' you will probably need to bump up a couple gauge sizes to get below 3%.
Make sure breakers and lugs will handle the upsized wiring. Select appropriate conduit size and have "fun".
