They are going to require a machine with the power to remove swirls. I wouldn't suggest anything lower than a Porter Cable 7424 for swirl removal. Those el cheapo $40 dollar buffers at Wal Mart are maybe good for applying waxes, but they don't do that well for swirl removal. You will want to get a PC. Since I'm a Meguiar's fan and it seems like that is what you are going to have access to, I would suggest getting some #83 and #9. Between the two of those you should be able to get the swirls out. #83 is more commonly refered to as DACP on Autopia. Its a 6 on the scale of 1 to 10 so that gives you an idea of how strong it is. Since Meguiar's is what you'll have access to then here is the whole scale:
#85 Diamond Cut = 10
#84 Compound Power Cleaner = 9
#4 Heavy-cut Cleaner = 8
#1 Medium-cut Cleaner = 7
#83 DACP = 6
#2 Fine-cut Cleaner = 5
#80 Speed Glaze = 4
#82 Swirl Free Polish = 3
#9 Swirl Remover 2.0 = 3
#3 Machine Glaze = 1
They don't list anything at the 2 rating that I know of.
That might help you figure out what you need. The product is relative to how bad your swirls are. I wouldn't suggest using Diamond Cut on a brand new car with light swirls and I wouldn't suggest #9 on an 8 year old car with terrible swirls. That's why DACP is such a great product. Its about in the middle and really effective against swirls. It removes them and doesn't just fill them so you don't have to worry about them coming back after you wash the car a few times.
Anyway, that is my advice. Get a PC and get some DACP. That should be a good start. There are a few sites you can order the PC and the pads and even the DACP if you want.
On a side note... where did you find P21S for sale in a store? Did you mean S100 or did you really find P21S?