There was a Virginia Civil War layout article in one of the recent model magazines, John, that might give you a lot of ideas. Sorry I can't recall which magazine or date. If your intent is to model a bit of the actual war, you might want to base your modeling around Salem, which was attacked by Confederate Brigadier General John Hunt Morgan's raiders in the summer of 1863, destroying or damaging many LNA&C railroad facilities there. Some of that destruction would be neat to model. Perhaps a visit to the Salem Museum and Cecil Smith would be in order.
As for equipment, solid info--much less photos--is pretty scarce, but the all-time locomotive roster in Hilton's Monon Route book can give you a pretty good idea of the locomotives around at the time, including their names (few locos carried numbers until after the war--and all were 4-4-0's, of course). According to the roster, LNA&C's last named loco was Achilles, built in 1865 and sometime after numbered 34. Other renumberings are shown on the roster, which would seem to indicate the road had 34 4-4-0's in 1865--but I'd bet they had a few 0-4-0's or something also.
Good luck with your efforts--and please keep us informed of your progress!