Congratulations. That should be a great machine. I don't have the 360, but I do have a 332. It was purchased new for my mother by my father in 1957. It's the machine I learned to sew on starting at about age 8 (I'm 50 now) and my mother gave it to me in the late 1980s when she purchased a new Pfaff. She has told me that almost immediately after she gave it to me that she regretted doing so as the new one just didn't compare. It has sewn so much stuff from silk to leather that I have almost worn the finish completely off of it.
It (likely if it's like mine) has a metal-cleated cotton motor belt as well as timing belt. Whenever you clean it or oil it be very very careful to not get any water or oil on that belt as it will cause the cotton part to fail more quickly. They have discontinued making the belts, so they are hard to come by. My belt has been replaced twice since it was new (once in the 1970s and once in the 1990s) and it is beginning to fail and I haven't found a replacement and I've taken it to three different sewing repair shops--have only seen some used ones on a UK site, but am wary of those.
It has a built-in camstack to do decorative stitches. There is a plastic stitch wheel that demonstrates how to make the different stitches. If your machine didn't come with that accessory, then join the oldpfaffphorum yahoo group and look at their files section and I believe they have a pdf you can print out and put together. They are also very knowledgeable in that group and can answer any questions you might have.
My old Pfaff has sewn things that other machines just quit on--including quilts made from denim and canvas and topstitching welt pockets on a leather vest that a commercial upholstery machine was skipping stitches on. Truly great machines.
Since I've had no luck finding a new replacement belt, I've been collecting other vintage machines to try to find one that would do what it would and the closest so far is a Necchi BU.
Enjoy your new toy.