Larger valve should be black water. Think large opening in toilet, large line to allow the lumps to go down. Smaller openings in sinks, shower so smaller line to let "water only" out.
I first fill the gray water tank so I have plenty of cleaner water to flush the lumps, toilet paper wads and/or other waste. It is always better to handle the sewer hose with it as clean as possible.
Edited to add: I always carry plastic/rubber gloves to handle the sewer hoses. After dumping I will pull one glove into a gloved hand and then remove last glove encasing the dirty gloves to pitch them into a trash can. I also keep a bottle of hand cleaner and paper towel to wash hands before doing anything else. And "never" bite finger nails.
Edited again to add: I will camp with the black water tank closed even if I do keep fresh water tank open and never, never open both black and gray valves at the same time. I think it best to keep black water waste in as much water as possible. I do not dump the black water until it is full. That way any floaters or other larger waste will be carried by the water down the poop-shoot. If I am getting ready to ride I will do a clean water flush before closing tank valves and then I put a few gallons of fresh water and chemical into the black tank so the water can wash the inside of the tank while traveling. I will also add gray water treatment to gray tank since it will be sitting until next trip.
Hope everything werks good and you can enjoy the trip.
Information overload. Sorry about that..