I use the thumbs wrapped grip, more stable, and can handle more weight. However, on all of my tricep exercises, I use a thumbless grip - even close-grip (22") bench presses. I think the triceps and lats are used more during the bench press movement, when using the thumbless grip.
As far as shoulder involvement, I think that depends on where you bring the bar down to - abs, mid pec, or upper pec. If you have a big arch and bring the bar low-on the abs, the shoulders are less involved in the lift - and it becomes more of a pec/tricep bench. If the bar is brought to the mid pec or upper pec, it becomes a lot more shoulder, which often leads to injury, or causes pain to an already injured shoulder, especially if you use a wide 32" legal grip. I've got 2 bad shoulders, but was still able to bench 500 raw and 570 with a double-poly shirt. I stay away from anything that aggravates the injury - like inclines or benching too flat or flys or behind the neck presses or side lateral raises.
And Spatts - nice forearms! 12" is impressive.