Wire Gauge/Type for 100amp detached Shop?
If it were me I would probably run 4/0 and mount a 100amp double pole breaker to feed it in your main panel. I'd come out of the breaker with #2 copper and then use a barrel connector to transition to the 4/0 aluminum on each hot line..  Then go the 200 ft in a conduit. In theory you don't need it that thick but I bet you would appreciate the less flickery lights when you turn on heavy loads out there.. You could also do direct burial, they make service cable that is approved for burial and you get a higher rating when buried in dirt because it is basically water cooled. 600v insulation, etc. If you make that trade off you may get annoyed every time you kick on a motor on.  They make ul approved barrel connectors for the transition from #2 coper to 4/0 and aluminum and Home Depot carries them.  The county inspector approved this method for me. I would call your local inspector and ask him. They are often helpful for the Diy folks when not swamped. Try again in early mornings before they are about, and try more than one..

Jeff