I have always used Meguires Gold Class for soap and Bleech-white for the tires. I need to order more of both but I wanted to check to see if there was something better out there
Car soap depends on what I'm washing, I'm going to order a gallon of Chemical Guys Maxi Suds here soon and give it a shot.
Cleaning tires I'll use bleach white w/ stiff bristle brush followed with blue Dawn if it's bad, otherwise just whatever soap I have in the bucket. For making tires look like a rich black I use Stoners aerosol tire shine and even it out with an applicator.
Meguiars - Gold Class for a 30 minute regular wash with Meguiars Hot Shine for Tires. I like it because its good for when I don't want to spend a lot of time on the vehicle.
Chemical Guys - Mr. Pink for the longer detailing days. Chemical Guys Tire Gel as well.
The 3 soaps I mainly use are Purple Power Vehicle and Boat Wash (Alkeline), Meguiars Wash Plus (deep clean and wax/sealant removal and synthetic clay lube), and Blue Coral for a cheap and decent prewash. I'll use either the BC or the PP on the tires as I don't use a dedicated tire cleaner or degreaser anymore -- the tire OEMs I've contacted do not recommend it. I also no longer use a dressing of any kind -- also not recommended. I'm more worried about tire longevity and performance than them being shiny.