I use 6 x 6's for decks even at grade level. Not that a 4 x 4 can't support a suficient amount of weight, but.....
On the west coast, we don't notch anything. Beams bear full on posts, with appropriate hardware for the connection. I generally will use 4x4 posts, if they are less then 6' tall, 4x6 or 6x6 when taller.