this is a good kit to start with
http://www.cleanyourcar.co.uk/polishing ... d_521.html
I would first wash the car then rinse,
dry the car.
use detailing clay to remove any paint contamination
wash, rinse and dry the car.
then use the above polishing machine with #80 on a polishing pad, if not then use #80 on the cutting pad.
if still not removing deep swirls then use #83 on a polishing pad first then still not coming out then #83 on the cutting pad (but as a last result)
Also you will need some polishing cloths and some lubrication like last touch.