I use Optimum No Rinse in a warm bucket of water, another bucket with warm water for rinsing and go one panel at a time with a sheepskin mitt. Wash, wipe off with microfiber and continue. Start at the top of the car and make my way to the bottom. I may empty the buckets and get new water/rinse depending on how dirty the car is.
I do the wheels sparingly - every other wash perhaps. I use ONR for them too except with a dedicated wheel brush.
If I got a ton of salt on the car I'd probably find a touchless wash (mainly to get the undercarriage). I don't have a need to drive for my job so I simply don't when the weather is bad. The problem with touchless washes is they use pretty strong chemicals so it will strip off whatever protectant is on the paint (wax/sealant).
This method worked well for me last year. No swirls, etc.
2011 BMW E92 335i - Le Mans Blue/Black, 6MT, M Sport package