Consider using the 2 bucket method to wash the car (one bucket full of your shampoo solution and the other with clean water). After cleaning each panel wash the mitt in the clean water before going back to the shampoo. Grit guards are also very useful. This propose will help reduce scratches on the paintwork.
Invest in a proper fluffy drying cloth.
Liquid wax is fine for a quick going over but consider a paste for better durability and protection.
Wonder wheels is fine for the occassional wash but is very acidic. Try something like Billberry which is milder and has excellent cleaning properties. Use a different mitt/sponge for the wheels and consider a wheel wax.
Also worth trying is a diluted shampoo mix as part of your pre-wash to help break down the dirt or snowfoam.
All that leaves is dressing the trim, tyres and glass.