In addition to the good advice given by Frayz...

True polishes have cut, 'pure' polishes have no cut. Cleaner polishes clean the paint without cut.

You can split proper polishes into three groups; abrasive (Poorboy's SSR1), solvent (AG SRP) and chemical cleansers (P21s Paintwork Cleanser).

As Frayz has said, unfortunately, from a picture like that no help can be offered as the camera will hide the imperfections. You need a high-res shot, close up, of the paint in bright light, to highlight flaws.
Unfortunately you won't get rid of the swirls by hand, but, careful use of the rotary will remove them. The downside to this, is often a rotary will leave marks, that will need to be taken out with a random orbit machine, which will leave no marks at all when used correctly.

A light cut polish like SRP will work better on a RO machine, and you'll probably get a better result over the whole car with this; a rotary is usually only necessary as a last resort for badly marred paintwork.

Gareth