Dawn dish soap will take wax right off. What kind of products are you going to use? I would take a look at Príma. It's what I use/d when I detailed cars. They have three levels of polish and an awesome wax. Used their stuff on my friends old faded cars and would bring the paint back to life. Also used it on the Lamborghini Gallardo, Lotus Elise, and Porsche my dad used to rent out when he owned an exotic car rental business. There a professional product that is priced to compete with the big brands like Mothers and Turtle, but IMO Príma is 20x better than any of those big brands.
Here's a thread I made about Príma:
The real key to polishing is keep the buffer moving. Don't want to stay in one spot to long and burn the paint. Other than that you can't really mess it up. Just have to be willing to spend time on it and have an eye for detail.