I would probably cross to one that's already mixed colored. Like Splash Barred, or maybe a Leaky Paint as examples.
These will help create more variety, or possible surprises.
Well, BB Red will just make more BB Reds.
Brown Red X BB Red Will make more Brown Reds. Back crossing will result in some BB Reds, & Brown Reds.
I can't find much info on Ginger Red, but from what I've seen they're BB Red with Db(Dark Brown), a gene similar to Columbian. It's a dominant gene...
What's your goal?
What available colors of hens/pullets do you have?
BB Red/Wildtype is an intermediate gene, it can be both dominant, & recessive depending on what it's crossed too.