If these swirls are circular, light will pick them up from any angle, and your paint will look horrible in the sun. If they are straight, they will be much less visible. Use a wash mitt with a deep pile to wash your car. Rags, towels, and especially sponges will trap dirt particles and scratch your clear coat. Stay away from wool mitts, as they cost more and scratch badly.
Many steps require soft towels.
I usually use between 4 and 6 towels to completely clean and wax my car. Don't use fabric softener on your car towels, because it may react adversely with waxes or polishes and leave a cloudy residue. By always doing everything in a the same order, you end up with a consistent routine that helps get the job done quickly and thoroughly. When you are leaning and stretching to get to those hard to reach spots, you may scratch a door or fender. Use a detergent designed for washing cars.