When I would install power to a customer's shop or other location, I would consider the load calculation before anything else is done- just like designing the service for the home to begin with.
As long as you aren't maxing out your existing 200 Amp panel at the moment (or using more than 50% at any one time) , you can run a 100 amp feeder to the shop without consequence. But the fact is, 90% of people will never use more than 50 Amps @ 240V in their shop at any one time even using a heavy use tool like a welder. You're only going to be able to use one or two tools at any one time, along with lights and possible a small heat source, so your load will be minimal at any one time.
To your question- 100 amp feed can easily be fed by #3 THHN/THWN . Voltage drop calculations include load estimates along with distance and the fact is you will seldom pull enough load for load drop to be a factor. If you would feel more comfortable #2 would be more than sufficient. For conduit for these conductors a 1" will handle 3- #3 conductors. Might want to jump up to 1 1/4" PVC for #2. Be sure to have a ground rod at the shop building and isolate the neutral conductor from the grounding/bonding bar at the panel as this will be a subpanel. It is also legal to pull a separate ground conductor with the feeders but I have found this to not be effective in breaker function at these distances.
Aluminum would also be fine as a feeder, but you would need to bump up the conduit size to accommodate the larger sized conductors. The cost difference will basically offset the difference in wire cost in the end.
^^^This^^^
When I was an electrician, many folks had no idea of "non-concurrent loads" and overbuilt as a result.
For that length of run, however, I would go one size conduit larger - for ease of pull.
Not sure, anymore, though - I've been out of the loop for 30 years (damn - that's 10 code changes!)
