claybar has nothing to do with keeping the surface free of swirls.
in fact clay will actually cause marring on the paint depending on the clay used.
heres the proper way to clean a car.
first off use quality wash media and soap. some good over the counter (because i know alot of you arent going to want to order online) is megs gold class, megs deep crystal, tw ice(i hate TW products but their car wash is just as good as any other).
also a quality wash medium.
a cheap alternative is this:
http://www.autopia.org/forum/car-detailing/98217-hey-grout-sponge-pusher.html
also a quality sheepskin mitt will work as well. if you cheap out, the results will show on your paint.
finally is the washing process.
dont wash the car in the sun.
rinse the car down well first.
use plenty of water/soap
use a spare bucket as the rinse bucket for your wash medium. this keeps the wash water clean and grit free
start at the top roof panel.
wipe down the entire panel, then rinse out the medium in the rinse bucket.
move onto the windshield, and from there the hood.
remember to always rinse the medium often.
go from the hood to the drivers side fender, and work your way counter clockwise around the car, (so youll be finishing on the front bumper)
if you drop the medium dont use it anymore until it is thoroughly washed. if you care about your paint, and keeping swirl marks and marring off your paint youll do this.
oh always use a seperate medium for the wheels. i use dedicated wheel brushes, and an old sheepskin mitt.
now onto drying.
the best way to get the majority of water off the paints surface, is to remove the hose piece, and let the water free flow on the paint. this will cause the water to sheet off rather than spash around when it hits the panel and make the water pool and bead up on the paint. so start at the roof, and just let the water flow onto the surface. do this on all the horizontal panels, and be careful not to splash to much water when hosing off the vertical panels.
because there wont be as much water on the paint, you wont have to use as many towels to dry it. i recommend a high quality waffle weave microfiber. the weave absorbs alot of water, and the high quality fiber will keep scratching and marring to a minimum.
it helps to blot the paint rather then wiping it down. this way you also ensure drying induced scratches are kept to a minimum.
its very hard to keep a car swirl free. but with the right steps, you can reduce the chances greatly.