Gun-barrel if the old license you have is a state that requires a hunters safety course you are good to go, the son taking the class in New Mexico will be good to go, as you said the other one will have to take the class.

Your 30-06 will be fine, there are a lot of counties that allow slugs so the slug gun will be fine, there are some though that are buckshot only, but I don't think you will have a problem finding ones that allow slugs.

Shots in Va will range from 5 yards out to 100's, most will be less than 100 yards though unless you are hunting mountains or fields.