If it is straight out of the body shop then i would not touch it for 2 weeks till the paint fully hardens. It worries me when people say the body shop moped the car, usually the y use a wool pad and G3, this removes allot of paint and results in Swirl city. You will never remove swirl marks by hand, dont even bother it will take you forever. It takes me 12 hours with my G220 on my car so it would take 3 months by hand. Best thing is to use a polish with loads of fillers. Auto Glym Super Resin is the best as already mentioned. Its the only decent product in the Auto Glym range.
If you are going to get a machine polisher it might be worth taking some paint thickness readings, you do not know how much paint has been removed by previous polishing. If you have never used a machine go for a DA as they are allot safer to use. Menz polishes are THE best IMO