Wiring a sub panel off of 100 amp breaker in my house breaker box.

I am building a shop behind my house. I want to put a 100 amp breaker in my existing 200 amp main breaker panel. It will go to either a 100 amp breaker box in the shop or a 100 amp main lug. My concern is what size underground wire I need to run between these panels. The run is between 175 and 200 feet. I want to maintain the 100 amps at the shop. I have been told everything from 2-2-2-4 to 4/0- 4/0- 4/0- 2/0. Also does this wire need to be run in conduit or will direct burial be alright.