Clean the wheels, tires, wheel wells. Wash the car with whatever you want. Whatever wax was once on there is just a rumor by now. Don't dry it, just start claying, the chance of it not needing clay is so close to zero there's no point and, you might not feel some of the contamination it would be good to remove anyway.
Then, whip out that nice rotary polisher you've been practicing with and cut out the light scratches. If you use the right pad and polish and have the right lighting you'll be able to see the number of scratches going down until just the deepest ones remain. I leave those for next time. Of course, I can cut to perfect, I colorsand show cars, but on daily drivers perfection isn't my method, I go for balance between what will make the car look as good as it can and leaving absolutely as much paint on the car as I can.
Then, once the scratches are gone and you have a nice consistent swirl, use a Makita BO6040 with an orange foam pad and, again, the right polish, and eliminate your swirls. At this point, the car should look waxed. It should be not only swirl free but pretty much cobweb free after you use wax and grease remover to check your work.
Once the paint is in that condition, wax it. Wipe the dust out of your door jams, again, with the right polish there shouldn't be much, but use a slightly damp cloth to pick it up, not just move it around, microfiber of course. Then take your wax off. Do the windows, treat the tires.
At some point in there, you should have done the chrome if it needed something more than just wax.
Robert