I don't know what that production red has in him, maybe RIR crossed with New Hampshire red? I doubt he has white leghorn in him since white leghorns are usually dominant white which means he would probably be white. I think there is a pretty good chance he would father sex link chicks. Don't know for sure though.
As to which white hen would be the best mother for this cross, I think it would depend on the specific line of white hen. Not all White Rocks, Delawares, Rhode Island White, or Light Sussex are created equal. Some lines have been bred specifically for specific properties like egg laying. If you can find a white hen with the silver gene that lays a big brown egg often, she will do. The way i understand it, not all White Rocks have the silver gene. Some have a dominant white gene instead.
I got Delawares from Cackle. They lay a fairly dark brown egg, large but not extra large. Probably 5 a week. I do not have experience with any of the other breeds.