I don't use the two bucket method or a lambswool mitt.
I prefer a noodle mitt as it holds more suds and lasts a hell of a lot longer than LW, especially when it comes to washing them.
Depending on what you need to do to the car will determine what you need product wise. If it has swirls or minor scratches you'll need a compound polish to remove them. Plenty to choose from, I prefer Megs Ultimate Compound. Easier to remove with a DA. You'll probably need to Clay the car. Use a G3 Clay Mitt, faster and easier to use, just dip in very soapy water and run across your paintwork. It'll sound rough but it's meant to.
Once clayed then polished you'll need to seal the paint. Again you're spoilt for choice. CarPro Cquartz Uk is excellent topped with CarPro Reload. Takes the hassle out of washing as the cquartz will put a Silica coating on the paint resulting in very little marks being applied to your car via washing.
Tyre dressing, my three favourites are Megs Tyre Endurance Gel, CarPlan Tyre Silk or Autoglym Vinyl and Rubber Care (apply with a paint brush). Don't by AG Tyre Dressing, its mince!
As said there's a full section of advice over on the Detailing Section. It's a very personal game and will cost you an arm and a leg but it's worth it. Good luck.