If you are looking to remove swirls, you need a DA at the very least. You wont remove swirls by hand unless you are Popeye, the best you can do is hide them.
You really cant go wrong with a DA. As Daryl (and his helpful link) say, start with the lowest cut (read finishing pad and non abrasive polish) and work your way up. As you learn more, you will know instinctively which pad/polish to use to get rid of swirls of differing degrees. Main thing is to start with applying glazes or other LSPs such as Dodo Lime Prime which have no or a little bit of cut, then you cant do any damage. When you are happy with how to use the DA, you can then try proper polishes and working up through pad types (finish pad, light cut pad, polish pad if required). You are removing tiny amounts of paint at any given time, its rotarys ability to quickly eat paint that is scary, but this isnt a problem with DAs.