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http://www.polishedbliss.co.uk/acatalog/car-care-advice.html
No affiliation, buy your products wherever they are cheapest but the car cleaning advice is excellent. It's a lot of reading to learn every step but worth it if you are serious about getting the best finish.
As said above it's the polishing step that will give you the finish you want. Just look at all steps prior to this stage as being proper preparation for this stage. If you don't prep properly you'll just make things worse as you want the paint surface as containment free as possible.
Machine polishing will give you the best finish but if you really can't afford one be sure to only buy the polishes approved for hand polishing or you won't be getting the full benefit. Many polishes need a lot of work to properly break down and give the finish they can provide. Some you just simply can't break down by hand.
The polish you buy very much depends on the type of paint you have. Jap paints are generally soft so you should stick to mild polishes for the majority of your work switching to medium for particularly poor areas.
Linus I'd recommend a medium polish on the panels you mentioned once properly prepared.
After the polishing stage you can use finishing polishes with fillers in if it has deeper swirls and then a good quality sealant to finish.
The professionals suggest sealants for white and wax for darker colours although often a sealant can be called a wax and vice versa so do some research.
We all have our favourite products but I won't endorse any as there will always be others that say something else is better. Just experiment with a few products people on here mention and figure what works best for you.
Hope that helps
