My suggestion would be to use two 5 gallon buckets for your wash and use the 2 gallon bucket for the wheels. To wash your car, fill one of the 5 gallon buckets with about 3 gallons of water and 2-3 ounces of your car shampoo...and then fill the other 5 gallon bucket with plain water. The reason for this is so that you can wash a panel and then clean out your sponge in the rinse bucket...this way you're not transferring dirty water back to the car.
Also, never use anything but microfiber towels on your car. Any other towels will swirl and scratch it. Our cars have very thin clear coats and they are relatively soft (which means easier to scratch). You can actually clay the car before you dry it if you want.
You have a great setup going...just a few tweaks here and there and you can wash like a pro!