For black and darker colored cars, its important to wash it outside of direct sunlight or at twilight. Or, get a product sold at O'Reillys behind the counter (they won't have them in stock; will have to order) from Superior Products called Formula 4 Spray Wax. You'll dilute it and spray it on the car after you wash and rinse. This will buy you time on water spots.
While you're buying SP stuff at the big O, go ahead and get the car wash soap, Dirt Buster. It is a higher pH soap that will strip OLD wax (contrary to popular belief, these higher pH products won't totally remove quality synthetic waxes completely, but more on that later), but the key benefit is it cleans FAR better than the typical OTC "pH neutral" soap. All that is marketing jazz that is designed to take advantage of people's ignorance. I still use Purple Power Vehicle and Boat Wash from Walmart, a little cheaper than DB, but DB dilutes a little better. PPVBW can be used effectively as a pre-wash.
If by two-bucket, you mean clean wash mitts stay in one and used mitts are thrown in the other then yes, use that method. If you mean what most people mean by rinsing the mitt in a water bucket and then dipping it back into the soap bucket, no. You never remove enough dirt plus you dilute the soap further. There are better ways to put soap on the car including foam canons and sprayers.
Once the vehicle is clean and dry, I apply a spray wax to it. I use Meguiars Fast Finish, but that may have been discontinued. I have 6-8 cans left, so I'm good for a while. Meguiars and other OEMs have a similar product labeled quick ceramic coating. Pretty similar stuff, basically. Apply this after each wash. Its easy -- at least on a car -- and if you wash it like I suggested above, you'll be applying a great finish to a clean car. Worrying about keeping a wax on a car is beyond old school. When I still had my Maxima, it took me 7-8 minutes total to effectively apply Fast Finish. Longer now with my F150 and a full size SUV might take half an hour with the roof, but nowhere near the hours long wax job of decades ago.
Anyway, that's what I do and recommend. People always complement me on my vehicles and how clean they are inside and out. I've found so many supposedly knowledgable car folks treat their cars like its the 1980s with respect to wash/wax, except maybe for the Ceramic thing -- which they'll pay big bucks for. I've never gone the ceramic route, but pretty soon, that's all that's going to be available. But the rest of it has evolved tremendously.