Well - first off. DON'T EVER USE DISH SOAP!!! I'm SHOCKED that the Zaino site said to do that. They should be shunned for that. Dish soap will discolor your plastic moldings - the alkalinity is made for dishes, not paint and plastic. Plus, it gets into the local drinking water, etc... If you are concerned about grease buildup, go to the store and get something that will remove grease from cars. Tar-off will do it. A citrus based cleaner will do it. Just don't EVER use dishsoap. It does more harm than good.
A clay bar is great, but is really only good for removing paint overspray and pollution. There have been many occasions where a clay bar was not able to remove stains from leaves and other imperfections. Rubbing compound may over do it, as a polish/cleaner might work as well. If you have tree sap, rubbing alcohol on a soft cloth works great. Just TAKE YOUR TIME. Let the chemical do the work - rub too hard and you'll scratch the paint.
Dude - you just spend $1000 on your paint and you want to save 5 bucks on claying your car? Come on - use your head. Products in the car care section of the local store have been developed for you car. Nothing else. Spend the extra 5 bucks - you get what you pay for.
Question - how had you been washing it before? Had you ever polished it with a cleaner?