Minimizing scratches is done with your cleaning products (shampoo, wash mitts, buckets), your drying (towel, blower) and your actual car care knowledge/cleaning process. I will try to make recommendations here across the board to help you minimize scratches.
Car Wash Method
Most professional details will recommend two cleaning methods below:
-Method 1: Get 2 5 gallon buckets with grit guards and 3 quality wash mitts (one for your wheels, one for the top 1/2-2/3 of your car, and one for the bottom 1/2-1/3 of your car). One bucket is for your shampoo (wash) the second bucket will be for rinse. After you use up the wash in the mitt, place it in the rinse bucket. Rubb it against the grit guard, then scrub it a little while you pull the mit out, ring it out, place it back in the shampoo bucket. Once you finish the section of the car that the mitt was designated for, set it aside. For example after your finish your wheels with the mit that was meant for the tires/wheels only set it aside.
-Method 2: Get a 5 gallon bucket with no grit guard. Fill it with your pH neutral shampoo then fill it with a boat load of quality wash mitts. The idea here is that each wash mitt has two clean sides to it. Once you have used both sides (basically once the shampoo runs out in the mitt) you set it aside and grab another mitt. This minimizes scratches because there is not dirt risk going back on the car, but I find this way over the top for most people.
I would recommend you pick a method above, buy the necessary amount of wash mitts needed for the method you picked, then do the following order. Power wash your car - hit it with a foam cannon - power wash again - begin cleaning your car with a pH neutral shampoo (rinse as you feel the need and keep your car wet so nothing can dry) - once finished cleaning dry the car (I usually work from top to bottom, but if the sun is heavily favoring one side of the car you will always want to address that first). For me I have a minimum of 3 wash mitts and I start with my wheels. The reason why is that wheels take time to clean so starting here can prevent water marks in the paint as well as prevent cleaned paint areas getting dirt splashed on them again. From here work your way with clean mitts from the top of your car to the bottom in sections (obviously take into account the sun). The owner of Ammo NYC has great youtube videos that are over the top in a lot of ways, but have great basic 101 knowledge for proper car care hidden in them.
Products
I am a huge believer in pH neutral products. They have good cleaning power while remaining safe for your cars body and coating/wax/sealant (no premature wear which means they can extend the life of your protectants).
-pH neutral shampoo: I have tested a lot of different shampoos, my two favorites are Gtechniq G wash and CarPro Reset. Both of them make quick work of every day grime and have great lubricity (meaning it glides easier for your contact mitt making it less prone to scratching while cleaning). They can also be used as a pre wash, though the results aren't near as good as something meant to be in a foam cannon.
-pH neutral pre-wash: Gtechniq W4 Citrus foam. It smells good, creates great foam when mixed properly and does a great job of loosening dirt/grime prior to a shampoo. It also will not cause premature wear on your coating/sealant/wax
-Wash mitts: Chenille mitts are fine and generally regarded as paint safe. I personally swapped to the thin microfiber strand style (like Gtechniq WM2 or Shine Supply Microfiber Madness) and I personally think they do a better job. Maybe it is in my head, but I feel I have noticed less fine scratches on my Black Mustang over time than with Chenille and that it does a better job pulling dirt deeper into the mitt. A quality wash mitt from a reputable company will also provide better quality materials (safer on paint and longer lasting).
-Towel/Drying: The safest way to dry a car period is with the metro vacuums master blaster car dryer with one Gtechniq's MF2 zero scratch towel. The dual stage 8hp blower does a great job of drying a car quickly with warm, clean filtered air. There are no contaminants that hit your car from this blower so it is the safest way to dry your car. I say pair with an MF2 zero scratch towel not because the dryer can't dry a car on its own, it can. It is just nice to have for speeding up the process in certain areas. This is an expensive route to go, one that is greatly worth it in my opinion, but not everyone will shell out $400 for this option. If you are going the towel route I recommend 2 Gtechniq MF2 zero scratch towels and 2 Gtechniq MF4 diamond sandwich towels. The MF2 is the most paint safe towel I have ever used. It is super soft, absorbs water well for such a soft towel and is a good all around towel with two different nap lengths (one side of the towel is for fine water drying the other side is for bulk water absorption). The MF4 is paint safe and my Mustang seems to like this towel better than the MF2 when it comes to water absorption as it leaves a streak free finish when drying where the MF2 can leave some streaks I have to go back for. The MF4 will take about 3 uses to get broken in for absorption, but once it is broken in it has far better water absorption than the MF2 imo. I usually use the MF4 for bulk water and MF2 for follow up's. You can just use solely MF4 towels or MF2 towels on their own though. I just usually do the pairing as it makes the process quicker with a towel.
-Detergent: Get Shine Supply Micro-Clean detergent for your washing machine. I have done tests on cleaning my wash mitts, applicators and towels with regular detergent vs this stuff and there is a big different. Simply put it makes your mitts and towels look cleaner, feel softer and extends their life.
This stuff should go a long way in aiding you with scratches. As always, you may want to entertain a good consumer friend ceramic coating like Gtechniq CSL (Crystal Serum Light) + EXOv4 or CarPro Cquartz UK to aid with protection from minor scratches, or you can give your car a quality buffing every year to remove scratches then hit with a pH neutral sealant/spray. I hope this helps.
Although there is almost no way to 100% eliminate all swirl marks just because we are not perfect and environmental conditions our cars are exposed to...but, we can eliminate a lot of them!
I have found that 100% clothdiapers (24" x 24") doubled up are the best for washing/drying....notonly in terms of price/longevity but the paint feels like it's been polishedeach time. FYI- the diapers must be flat fold (meaning no seams) and washed 3times (typically) to ensure softness and absorbsion and outperforms the microfiber wax removaltowels consistently- cheaper, better, last longer, gives a much bettershine/result.
The absolute best washingdevice known to man is a long boar hair brush....yeah it's stiff when dry butwhen wet, it is softer than any cotton towel you could find & because ofthe tips only touching the paint, the swirl marks are almost 100% eliminated.Available at griots garage or Erie Brush & Manufacturing Corp, 860 W.Fletcher, Chicago (but you need to have a company name to purchase, noindividual sales) .
The next best option, 100% cotton diaper (Babies r' us has em- about $20 for abag). Doubled or tripled up, wash them 2-3 times with fabric softener beforeusing them for washing & drying. For washing, without contact dirt on thevehicle, use the open butt of a garden hose, on low to apply water just aheadof the wash diaper....it almost makes the towel float and the remaining dirtfloat off the paint without touching.
Soap...I recommend: No7 Car Wash Concentrate
OP. I would advise against this outside of the boar's hair brush, which can be found at any reputable online detailing orientated store (detailed image, autogeek etc etc). They are useful in and out the car, but only in recommended areas. Things like cleaning your leather seats, or exterior pieces (Audi 4 rings logo for example) that mitts have a hard time reaching thoroughly. I would also never use No7 Car wash, especially if I had a sealant. I don't care what they say, it will strip your protectants/sealant prematurely. Not trying to be rude to beechkid, but I would never do 90% of what he posted to a car. There are a wide away of products out there and they are all not equal.