Remington, Mossberg and Benelli in that order.
The Benelli will probably be the lightest but to me that is a moot point. I want the weight for recoil management.
Shitcan the pistol grip, they look cool but suck to shoot(just how big are your wrists anyway) plus you lose the ability for a good shoulder mount. You can always tuck the stock under your arm for mobility if need be.
If this is a HD shotty "spray and pray" from the hip is a poor tactic.
Saddle mount for the rail but shitcan the Eotech if you are concerned about weight.