As with all things, a machine polisher has its place. A man just has to know it's limitations.
I don't think anyone sensible would recommend using a machine more than three or four times a year.. but you can only fix some paint defects with a machine and if you have the right equipment, you can't really do any damage, so don't be worried about it.
A dual-action machine is the place to start as it's a lot kinder to the paint than a rotary polisher. Rotaries are used by professionals as they are quicker (i.e. much more aggressive) so stick to a dual-action.
Polish is also significant in the process. Too fierce a polish will eat your paint up. Don't use anything more abrasive than it takes to remove the defects you're faced with.
If you just want to shine up the paint, use the mildest polish in the range you choose.. e.g. Poorboys SSR1 is very gentle. Other brands have their "fine" polishes too.
If you're trying to shift a defect (e.g. swirls) you may need to go to a more abrasive polish. These remove more paint (the layer with the defect in) but should then be followed by the "fine" polish to finish.
With a "fine" polish and a DA polisher it's practically impossible to wreck the paint.
The next thing to worry about is the pad. Pads come in different levels of abrasiveness too.. Cutting pads, Polishing pads, Glazing pads.. you name it. Don't get too worried by this.. if you're starting out use a light polishing or glazing pad and again you can't miss.
If you wanted to become an anorak you can mix polish and pad cominations to give you any possible permutation of "cut".. but in reality you won't notice the difference the pad makes, using the same polish and machine.
1) Find your website that sells all the stuff you can possibly want..
2) Select a machine to buy (Kestrel and Meguiars G220 are splendid kit.. Porter Cable is a very well regarded US jobbie .. but it needs a transformer for its 110v motor. Don't **** about with all that, the Meg's G220 is essentially identical to the PC).
3) Choose a "brand" who sell the different grade polishes in an easy-to-understand format (e.g. Poorboys do SSR1, SSR2, SSR2.5... each more aggressive and easy to understand naming system)
4) Buy the least abrasive/finest polish (and, if you have a lot of swirling.. the next one up too).
5) Buy a couple of polishing pads (or a polishing and a glazing pad)
6) Prepare the car.. (wash, dry, clay, rinse, dry) then polish it with the finest polish and the finer pad. If the marks aren't coming out, go to the more aggressive polish and pad. Then finish with the finer polish/pad.
7) Buff out the residue.
8) Wax it, Wax it, Wax it... as the paint is now all fresh, smooth, shiny and more importantly "unprotected".
9) Enjoy... though it'll be midnight now.. so you may have to pop out tomorrow morning to really appreciate your efforts.