to remove swirl marks, you need a polisher. it depends on the depth of the swirl marks. there are strong polishers and weak ones. try using a few combination, polish and pads and see which one works the best. remember those are 8hours minimum job if you want to do it right. menzena are good polishes
and yes, you will probably need a machine. They will give way better results compared to hand. and by hand it takes forever. take into account that you will also have to use a pre-wax lotion(because its gonna be like first time waxing) followed by a good waxing after that!
yea it is necessary to claybar the surface before polishing, because even if you gave the car your best wash, there is still ALOT of invisible contaminants left on the surface. you don't want to drag those in circles on your paint job as they are the ones responsible for swirl marks
i hope i answered your question. i am not a detailer, and please feel free to correct me if i'm wrong