With regard to polishing, just use any polish recommended on here and you cant really go wrong by hand. The abrasives in them are so minimal, unless you are using a machine polisher, you cant exert enough pressure to work them in too much. Most also have diminishing abrasives, which mean as you work them, they break down, meaning you can never rub them in too much. Something like Dodo Lime Prime, by hand, you cant do it wrong
Goes without saying that you should use a good clean microfibre cloth to remove it, and keep turning/folding the cloth.