I am guilty! Yes I am bit OCD with paintwork, not only because I like it looking clean, but also IMHO it also protects the paintwork and in doing so, reduces body rust.
Anyway, get yourself a cheap polishing machine (not one of those big mop type one's) that look like an angle grinder in shape such as
https://www.argos.co.uk/product/8647300Get yourself a few velcro backed sponge heads.
Get yourself a selection of cutting compounds and glazes - I use Menzerna but there are plenty to choose from.
Get your car washed, ideally with a traffic film remover, so you get rid of the old waxes. (Washing up detergent also works)
Clay your car to remove the stuck on contaminates. Blutak and a spray of water as a lube works OK
Start with one panel and using the machine, polish in stages until you get a decent finish.
You will NOT damage or burn the paintwork unless you keep it in the same position, on its highest setting for al least ten minutes.
When you are happy, give it a coat of wax or sealer to protect it over the coming months.
If you live local to Bristol I am more than happy for you to pop over for a demonstration. With a bit of practice... (SAAB 9000 Amethyst)