The first P-47D-25-RE models (the 1st 'bubbletop' version) were received in May 1944. The 56th Fighter Group would be a good one to focus on - plenty of aces and history there, plus they were among the first to receive the 'Superbolts', as they called them. The 56th is the group known for keeping its P-47s when the P-51 was being rolled out to most of the groups. Also as an interesting side note, the 56th eventually became the collection of training squadrons at Luke AFB which trained all of the F-16 pilots for the Air Force (they're currently being reorganized as the Air Force transitions to the F-35)... end side note.
The squadron received a trickle of the 25-REs, so as you said, the first went to group and squadron commanders. The first five went to 1) the group commander, Col. Zemke 2) Maj. David Schilling and then squadron C/Os 3) Capt. Don Goodfleisch 4) Maj. Lucian Dade and 5) Maj. Francis 'Gabby' Gabreski.
Here is Col. Zemke's plane (42-264413 / UN-Z), the very first 'bubbletop' received by the 56th, now preserved at the American Air Museum in Britain:
Source:
www.airport-data.com
It's hard to say exactly how many were in service on June 6th. Probably not much more than the C/Os and perhaps their wingmen. The 56th FG didn't have enough of them to take advantage of their additional fuel / range until August of '44, if that tells you anything.
They would have arrived as 'unfinished' (i.e. bare aluminum). Since the landings and subsequent basing on the continent was expected, they ended up being painted a variety of camo schemes. Of course the D-day strips would have been applied if nothing else.
Source: Pinterest
I'm not sure on the accuracy of the above. It could be and looks right, I'd just double-check before basing a model on it. But it does give you an idea of how an aluminum finish would look after squadron markings, D-day stripes, etc. were applied.
My advice is to research the C/Os and their aircraft and pick one of those. Gabreski as a well-known ace is a common choice for the P-47, but the others are fine choices as well, especially if you want something a bit different from the norm. In any case, many model kits will use Gabreski, so he can still serve as a guide for the model kit selection.