I would not put two new tires on one side of a dually with 2 old tires on the other side. The spider gears or clutch pack in the rear end would be constantly working in straight line travel. The spiders might be OK but the clutches could overheat.
If that is your required buying pattern then you might be better going 1)2 front; 2) 2 inner rear then move new front to outer rears (keep the best old tires for the front); 3) 2 fronts to complete the change.
Good luck with your tire search. I like Coopers. I also like Discount Tire Direct for good prices and quick delivery. I have a good shop nearby that does all my mounting and balancing. The internet places usually have suggestions for local installers.