I built a new shop, pole building and need to run electric service to the shop. The pole with the transformer and ct meter that I will share with my residence is 190 ft. from shop. Total length of cable from transformer to sercice panel will be 218 ft. I will run this underground in appropriate size PVC conduit. For a 200 amp service will I need 3/0 or 4/0 wire.

This will typically be sized by your power company, but 4/0AL or 2/0CU will most likely be the size they require.