Never seen Band of Brothers. Saving Private Ryan gave a better picture of what life was like for a soldier, The Longest Day was, as you said, perhaps a better account of the D-Day invasion.
Toby Keith's video "American Soldier" features reenactments of American soldiers from various wars, including a doughboy wearing that recognizable WW I helmet climbing out of a trench with a bayonet and charging the German lines. It's nice to see WW I being memorialized, since it's usually the forgotten war.
Band of Brothers is on DVD. I highly recommend it.