wouldn't dust the car as the first step.
would just rinse the car with water very well

would then use car wash soap and a strong hose to clean in the wheel wells and the bottom of the rocker panels plus the bottom of the bumpers front and rear.

Then do an extensive rinse of the body with water, then use the dishwashing liquid to strip old wax.

Then I would use a quality rubber protectant on all the rubber trim after using the dishwashing soap.

I would then clean the wheels, but I wouldn't detail the wheels with wax till the entire body was done.

When using simple green and dishwashing liquid. For the dishwashing liquid in a five gallon bucket I would use two cap fulls. I realize the kind of cap it is.
For the simple green I would dilute twenty : one and see how that works.
Exchange the buckets with new water and cleaner frequently. May even want to use a second bucket just to rinse off your towels.

You can never have enough towels, wet towels with lots of suds are nice for cleaning in the door, and trunk jamb. Extra towels for drying and waxing make for a much easier job.

Use the applicator that came with the wax and once you drop it on the ground use your towels.