For removing dust--KozaK cloth.
For spray detailing--Meguiar's Mirror Glaze 135 Professional Synthetic Spray Detailer and Meguiar's M9910 Ultimate Wipe microfiber cloth. I like this better than the other Meguiar's cloths. As of the last time I spoke with Meguiar's, the M9910 was on back order. If you find one in a store, make sure it is "edgeless." This same product number was used for an earlier cloth that has a black border. The latest version is much better.
For waxing--Meguiar's Mirror Glaze 26 Hi-Tech Yellow Wax. I use the paste. It is also available in liquid. I tend to get liquid all over myself. I apply the wax with a Meguiar's Even Coat Microfiber Applicator Pad. I remove the excess wax with an M9910 cloth.
For claying--Griot's Garage Paint Cleaning Clay. I use either Griot's Garage Speed Shine or Meguiar's Quik Detailer as the lubricant. I remove the excess with a microfiber cloth. Note: Do not use the Meguiar's 135 as a lubricant for the clay. Meguiar's says that this has too much lubricity for use with clay, and can keep the clay from doing its job properly.
For interior--Griot's Garage Leather Care for the leather and a damp towel for the vinyl.
For windows--I'm not pleased with my window cleaning. Part of the problem is that I can not see any streaks that I might have left because of lack of good lighting in my garage. I use a professional type 12" squeegee on the outside, and wipe off the streaks that I do see with a microfiber cloth or lint free towel. I often use Griot's Garage Window Cleaner, which I like a bit better than Stoner Invisible Glass, but it's pretty much a tossup. For the inside, I don't use the squeegee and just use a microfiber cloth or lint free towel with the cleaner. For the interior of the backlight, I use one of those triangular shaped tools with a microfiber bonnet with the cleaner. The tool makes it somewhat more convenient to reach the window.
For wheels--Just a spray bottle of distilled water and a cloth, with an occasional wax job. My wheels are painted, with clear coat.
For tires--The latest product I used was Armor All Original. I have used products specifically designed for tires, but found that the excess tended to get thrown off the tires and onto the paint when I drove. Since my car is white, that doesn't look good. I'm still looking for a product that I like a lot.
I do not have a power buffer.
I have not felt the need to use any polish or cleaner/wax on my Mustang yet. On previous cars, I had excellent results with Meguiar's Mirror Glaze 7 Professional ShowCar Glaze if I wanted a non-abrasive polish. For a slightly abrasive polish, I used Griot's Garage Fine Hand Polish. I don't rate this as great, but I haven't found anything I really like. If you want to use a cleaner/wax, I recommend Meguiar's Gold Class Wax. It is available in liquid and paste. I used the liquid, even though I made a mess, because it is supposedly better. I read that Meguiar's Cleaner Wax can cause hazing, particularly on dark colors.
I can't help you with washing suggestions. I've had my car for a year and a half and it has never been washed. I don't have the facilities at home for washing it, and I'm not going to take it to a commercial car wash.
At least insofar as hand cleaning goes, foam pads are OUT for pure waxing of the painted surfaces of the body. Foam pads are good for applying a slightly abrasive product. Terry cloth towels are OUT for use on the painted surfaces of the body. They can be used on the wheels and for wiping down the interior. Microfiber is IN.
If you want to try any of these products on my car before you use them on yours, please let me know. lol