wire size for a 150 amp sub panel from a 150 amp breaker added to a 400 amp main panel
For your 150' run depends on whether or not you use Copper or Aluminum (aluminum being cheaper).
You would need 


Copper        1/0 @75 degrees C or better 90 degree c 
Aluminum  3/0 @75 degrees C or better 90 degree c


http://www.cerrowire.com/ampacity-charts

Grounding Panel to the building - the following article gives a more complete answer than I should write here. 

https://fyi.uwex.edu/mrec/files/2011/04/W4.-Biesterveld-NEC-grounding-MREC2010.pdf

NEC code section 250 should be of some help to you.