I have an ice chest with ice and water to put the birds in right after I butcher them, so ice water. I typically do five or so birds at a time. By the time I've finished the ice may have melted but the water is still cold.
I cut the birds into serving pieces as I butcher and put the pieces in a bowl of water on the table as I butcher. The liver goes into separate yogurt cups for the dogs. My routine after I put the last piece in that bowl, I kill the next bird, then rinse my hands. I then put the last bird in the ice water cooler, rinse off the table and cutting instruments as the bird is bleeding out.
I do not brine or age my birds but put them in the freezer right after butchering. I do thaw them early and let them age a few days in the refrigerator before cooking. That works for me. Some of that may depend on age and sex of the birds butchered. I butcher dual purpose cockerels and pullets mostly, with an occasional mature hen or rooster. The older birds get cooked differently.
Aging, brining, and marinating are three different things, though some people combine aging and brining.
Aging is when you keep the bird in the fridge or ice water long enough for rigor mortis to pass before cooking or freezing it. It's probably best to do that before you freeze it but logistically it's easier for me to do that after freezing.
Brining is when you soak it in water with a certain mixture. Many people just use salt (in different amounts) but there are some different recipes that might use something else. Brining will affect the flavor some, depending in what and how much you use, but the salt makes the bird hold moisture. Depending on how you cook it that extra moisture can make a lot of difference. It's probably a really good idea if you fry, grill, or roast it but if you bake, stew, crock pot, or pressure cook it brining probably doesn't make much difference. You can always add salt afterwards.
Marinating is when you soak it in an acid before you cook it. You can make your own marinade, usually based on vinegar or wine, or you can pick up a huge variety of sauces to use at the grocery store. Marinade adds flavor, of course, but it helps break down the fiber, making it more tender. The longer it is in a marinade the more the fiber breaks down. Too long and it might become mushy. To me the Cornish X are butchered young enough that I don't think they need a marinade but it can really help older birds.