What size copper conductors do I need for a 200 amp panel approximetly 150' form the pole.

Thank You,
Brian

For a single family dwelling, #4/0 aluminum will be fine. If the main breaker is at the pole, then use #4/0 4 wire URD direct burial cable. If the main is at the panel, only need 3 wire. If not for residential, let me know as the wire size will be different.

Grounding is also different depending on the location of the main breaker.

I would use 3/0 copper. Depending where you live, aluminum may not be allowed.
For 25 years, I have never used aluminum, but have repaired many aluminum related problems. Personally I would use PVC. And while trench is open, I would have a couple of 3/4' PVC for Phone, Cable, Sat, Camera, Computer, or Alarm wiring. It is more expensive
Than above method.