Of the products that you listed there will be very little if any advantage to using the PC.
Klasse AIO is a chemical cleaner that will do little defect correcting. Klasse
SG needs to be applied thinly to be able to buff off. Both applying and buffing are just as easy doing it by hand as to use the PC. The P21S is IMHO definetely easier to apply and buff off by hand.
Using the PC you might consider purchasing an abbrassive polish for defect correction. FPll, IP from
menzerna. The SSR line of products from poorboy's. Just to name a few. There are a whole host of product available. Am not sure of availability of products in the UK. I am sure that someone will suggest something that can be available to you.