eblend what do you plan on running on 240? Heater? Welder etc?
Best to run a heavier wire #8 or even #6 as you can always run a lighter breaker and receptacle, but can't go the other way.
I ran #6 but it's because I have a 60 amp buzz box in my garage and I wanted to be able to crank it.
Normally for heat etc. #8 and a 40 amp breaker should be plenty.
Typically you would just put a 4x4 box on the wall and then change out the receptacle to a dryer or range one depending on what you are running.
2017 VW Jetta 1.4T (winter car)
2010 F-350 Nortruck Tool Shed
2007 BMW 5 (Wifey's)
2004 Audi A4 1.8T 6spd Stage III w/ Meth
1985 F-250 6.9L IDI w/ATS turbo