happy birthday, nice gift.
your going to want to get a liquid compound, i used turtle wax liquid compound heavy to medium, it cost under 10 bucks. it will take out the swirl marks and get rid of the haze, it will look like it was waxed, but its only compounded. then wax it, you can get a soft foam pad to put the wax on, any wax will work. and the buffer works it in better.
dont stop working a section until the compound is dry, when its dry, wipe it off, ( you'll figure out how much compound you need for a section after a few passes) it should come off like dust, no real rubbing needed. same thing with the wax work it in till its dry, then wipe it off.
good luck, take some pics, before and after when you get to it.