I am planning to run 240 volt service to a small shop about 50 feet behind my house through a 50 amp breaker in the main panel in my house. What wire should I use?

Are you thinking conduit or direct bury? Makes a difference.

Thank you. If I can use direct bury it might be simpler although I would still have to use conduit through the sides of the buildings and down below ground level. It is not a direct line from where I will have to go into the buildings as I will have to ditch around the end of a sidewalk that extends from the side of the house a short distance. I forgot to include that in my question, so I remeasured and the run will be closer to 65 feet from breaker box to box.

UF-B can be run through conduit for protection. However, it is not just Ampacity, it is rated on how it is used. For example, if you are going to be running motors, you need to multiply their amperage by 125% for total amperage. Straight amperage for 6/4 UF-B is 55 Amps. However, if you are going to be running a lot of motors at the same time you may need to increase you breaker size and then upgrade to 4/4. What are you planning to be using? Voltage drop would be minimal, less than the maximum 5%. With a subpanel you will also need a separate grounding rods, 2 of them at least 6ft. apart, at the shop. Read up on installing a subpanel before buying the wire. In older days you could use a 3 Conductor.

I will be doing hobby auto work mainly. I will have fluorescent lights and bench grinder along with drills and hand held buffer, etc. I would like to be able to use a small welder at some time.

You should be OK with #6/4 to the breaker box.

Depending on where you are located this likely needs a permit and they would require a sub panel inside the shop.

Thank you for the info.