Yes, your order is right. You wash, then clay, then polish, then wax. Definitely use your PC. With the right pads and 3M Swirl Mark Remover, you should be able to take the waterspots out and making your paint look like brand spankin' new. Using your hand is alright too, but you won't be able to make it look really good and your arm will be really really dead. Trust me, I've done this before then I spent $110 for the PC. That thing made my life sooooo much easier!!
Get the pads at this site
http://www.properautocare.com/hipadkitwive.html . They know everything about car detailing and as a customer from them, those pads are incredible!! Price is a little steep, but it's totally worth it!!