Some folks will tell you not to squeeze the grains because it releases the bitter tannins within the grain husks... I've always been told not to squeeze, but I don't see any real harm in it... You may have a slightly more bitter taste.
I just sit my grains in a strainer over my brew pot and let it drip for a while after sparging. Then I give it a couple shakes and put it in a plastic bowl. Then when I add my extract and get that stirred in real good, I come back to the plastic bowl and pour in whatever else dripped out. Then the grains are off to a holding bin ready to make grain cookies. I'm an extract brewer so far, so I usually only have specialty grains.