Was afraid of that. I do worry on using one that is my issue.
If you are careful and don't go too agressive, the risk is actually pretty low.
The first time out, I went very gentle on the car and actually didn't get the level of correction I wanted, but I learned a lot about handling the polisher, when to swap out pads, applying the right amount of polish etc. The best part was the car still looked much better, so I felt successfull in the work performed. Each time since, my skills and knowledge has improved.
The Meguiars Ultimate polish recommended is a great starting point. It's pretty mild, easy to use, cheap, readily available in stores, and knocks out swirls with good results on soft paint. For me it was the "gateway polish" to exploring other polishes. Combine it with a mild to medium polishing pad and you should be able to safely remove swirls with pretty low risk to your vehicle. If you want to lessen the risk further, try an AIO product like 3D Speed, Griot's One Step Sealant, or others sold here. The abrasives will be a bit more mild and they add protection at the same time. The only negative is you can't put a coating over the top of them.
I'd also encurage you to watch some of Mike Phillips video's. I don't remember if he has one for beginners using a DA polisher, but just watch him demo just about any AIO or polish. He always uses the same technique when polishing out a surface. I'm sure there are other's who have done good video's, I just happened to learn from Mike's.