Where are you originating from? Virgin is nice but you'll probably be flying out of JFK which is a pretty short flight in real biz class. It also means a shorter domestic DL flight to connect, then two domestic European flights in glorified coach class. Air France and KLM don't gave flat bed seats, so you should probably stick with DL, Alitalia, or VS. You should be able to book entirely through delta for a combination DL, VS, SkyTeam flights.