Here is my suggestion or my 3 step process during the spring / summer months,
During the winter I only go through the Touchless do get dirt, sand and salt off the car. You're not going to have a showroom look in the winter... at least in NH we're not. I imagine it's going to be the same in MI.
1. Take it though a touchless - you my have to do a google search to find one in your area. Or at least use a pressure wash bay, They get most of the dirt off... The real abrasive stuff like sand, dust, salt, etc...
2. Once this is done, I usually get a bucket of cold water and two sponges (I don't use soap) I start with the top of the car (roof, trunk and hood) and then move to lower parts (doors, fenders, undercarriage) and basically give the car a cold water sponge bath. Rinse the sponges often. I use this method because it eliminates having to hook up a hose, soapy buckets, soapy sponges and, if you just give it a sponge bath after a touchless rinse, the wax will remain on the car from the touchless /pressure wash.
3. When done, dump the water and refill with fresh cold water... Rinse the sponges and and ring them out really good. Go back over the car using the sponge to get excess water off the car (basically dry it). Constantly ring dunk the sponges in the fresh cold water and then ring them out again and continue to dry the car.
This will keep whatever wax was applied at the car wash, but will get the layer of dirt off that the car wash didn't get.
Personally, I only take a car through the full car wash when it's usually 5 years old and probably ready for trade... just cause I get lazy and don't really care any more.
But while it's still new (and being paid for) I usually use the 3 step method mentioned above.