Simply put, there is no "quick way" of cleaning a car without getting swirls on it; reducing swirls really depends on how much time/money you're willing to spend.
gilmour foam gun
decent car wash soap(Turtle Wax Ice at Costco)
3 microfiber or sheep skin mitts (for cleaning car)
p2s1 wheel cleaner
EZ-Brush for wheels
package of microfiber drying cloths, applicators, buff-off cloths
pinnacle souveran w/ polycharger
Flex or any random orbital polisher (if polishing)
I would first spray the car with water then follow through with foam. Let it sit for several minutes~while waiting clean the wheels with p2s1 and the EZ brush. rinse the car. follow through with another thing of foam but this time do the 2 bucket drill of cleaning (i use 1 mitt for roof, another for trunk/bumper/ hood and the last for doors). then you dry. if you havent clayed your car yet do so but use a fine grade clay cause it doubt your new paint has that much contamination. Polish car if necessary( use halo lights to help you;bought mine for $25 at Lowes) Once no swirls use Jetseal, do 1 thin layer and let it cure~i usually give it a day, use microfiber applicator and buff off using microfiber cloth. afterwards i follow with a layer of wax i personally use pinnacle souveran w/ polycharger, again use microfiber applicator and buff off using microfiber cloth.