The hardest part is sometimes working out what the "blemish" is first so that you can do the right next step. Basically - is it damage in the paint or something that needs to be removed from the paint?
Claying is a paint decontamination process to remove contaminents stuck/embedded in paint (/lacquer) which are not removed by other cleaning (e.g. shampoo, tar remover, iron fallout remover). If used properly they won't remove significant lacquer but they are a very mild abrasive. Because it's quite time consuming you also probably don't want to be doing all the time. As with any deep clean process, getting protection on afterwards is crucial or you can be worse off.
Polish is designed to a similar job and different to "wax", but confused by many products being a mix of the two. That is they're designed to have a mild abrasive affect to remove contaminents (and possibly even very very marring of the finish) which the cleaning process does not. Many of the consumer polish/waxes will also contain fillers to mask blemishes - these wash out on the next wash usually and you have to reapply. Ever seen amazing demos on TV or at a show where they apply a polish to a knackered bonnet and its like new?
I've personally after many years/products given up on waxes and moved towards the newer nano sealants, but I don't want to get into specific products as that often starts religious wars!
Back to your question...
If you're starting with an unknown quantity with the condition of the paint there's no quick fix other than perhaps some of the coloured polishes which contain fillers to mask/improve blemishes. If that sounds good enough, then stop reading now before I go into the full horror and obsession of a more complete approach...
If you want to sort it properly, you'll need to set aside possibly 1-3 days depending on how far you want to go or how long you're able/want to work in a day. It could be more if the blemishes need more major work. Indoor space helps greatly.
With that time you could:-
Deep clean - wash (probably more than once) and use something stronger than shampoo on parts which require it - e.g. an All Purpose Cleaner which can be sprayed on to dirty/greasy parts.
Go over at least the lower part of the car with tar remover if needed (claying will get some off, but this is easier and will make claying quicker). Suggest having the tar remover in a spray bottle rather than applying with a cloth - for some reason it just works much better. Spray, leave, then go back over with a bit of extra spray if needed and your microfiber to remove the tar blobs.
You can do iron fallout remover, but will often be OK without this (different story if deep cleaning wheels prior to protecting).
Clay next.
It's well worth also making up a mixture of Isopropyl alcohol and de-ionised/distilled water in a spray bottle. It's a very good final cleanser which dries on its own and leaves no residue so that whatever you put on to protect the paint sticks better/lasts longer. But it has a number of general cleaning uses and can be used with a clean microfiber to see if your "washed" paintwork is really clean.
Use this spray to clean the paint of the claying residue (even better - do another quick shampoo after the claying - it will be easy and fast as teh car is much cleaner/smoother - and then use the IPA spray).
At this point you should have very clean paint. You can then inspect and decide what you want to try and tackle. This might be marks in the paint left by insects, water marks etc. You will probably also have anything from swirl marks, to scratches and stone-chips.
The minor stuff can be tackled through some hand-polishing/cutting, but if the whole car needs doing, my suggestion would be:-
get a pro to paint correct if you can afford it (it's typically a one-off job if you then look after the car), or
invest in a dual action polisher and learn how to use or
accept that you will not be able to fix these issues and go back to using something which will make it look better but needs a fair bit of topping up.
For cutting polishing, start with the most gentle product and work towards more aggressive products. So any of the high street polishes which you may have as the lightest first touch working towards heavier polishes and then scratch removers cutting products. Let's leave aside wet-sanding etc for now.
You specifically asked about cutting polishes. For what it's worth I go with what I have in the garage which occasionally expands:
Some Mer which I gave up using years ago for general use once I realised what it was doing, but which is still very useful for light polishing - I clean off afterwards with IPA spray as only want to use it as a polish and don't want teh rest of it left on the paint as I apply other protection - inefficient but I have a lot left over!
Farecla G3 paint renovator
Farecla G3 scratch remover
The two above are from the consumer range which Farecla started selling through Halfords. I bought them because I'd had some small quantities of G3 compound from Paints4u as part of touch-up kits. It's magic when used as part of a process where you flat touched up lacquer with wet sanding and then use the G3 by hand to bring back a gloss.
I don't find either of the Farecla products from Halfords to be anywhere near as good. In fact Halfords own brand rubbing compound in a yellow squeeze tube is closer to the G3 that I had from Paints4u - but if you have time it's worth ordering some G3 from Paints4u or elsehwere. I probably can't post links, but go to that site and you'll find Farecla on the left and then look in rectify compounds.
I also have Menzerna medium and heavy compounds for use with a dual action polisher. No particular recommendation as I'm new to that stuff and this is just the first stuff I've tried.
Take any of the products listed above with a pinch (although I do think the G3 is excellent if doing a flat/polish bit on lacquer), but hopefully the principles/process may be of some help.
To be clear I'm just an amateur who has gradually learned and still has a lot more to learn. You can get better advice if needed on more dedicated forums. I'm a big fan based on experience of G-Techniq products. They have a polish (P1) which is meant to be very good and is suitable for hand or machine use, but I've personally not tried yet. May be worth taking a look.
Cheers
Stuart
