By which I mean, like really really polish a car. That showroom type finish where all the surfaces are like mirrors. What are the processes and products involved? I would normally just pay someone to do it, but this is a twenty year old car with a couple of rust spots (but otherwise in mostly reasonable shape), with sentimental/collector value, and I'm kind of precious about it and don't trust a valet service not to chip paint into the rust.
Well, these smarty pants are not going to be any help.
To get the kind of shine you are looking for you need to repaint the car. And the type of repainting that will give you what you want will cost you about $1,000 (USD), or more, actually you can spend $5,000, if you want to. That will give you a beautiful multi-layer paint job, like you see in magazines and car shows, where they first sand the car down to bare metal, then bondo the rusted out parts, then spray the entire car with primer, let it dry, then spray with paint. Then clear coat, then dry, then paint, then dry, then clear coat, then dry, then paint, then dry, then clear coat, then dry, you get the idea. They will keep going, as long as you are paying. The more coats, the "deeper" the shine. If you've ever heard of a 12" shine, that's where you hold a ruler up the car, and see how much of the ruler you can read in the reflection. If you can see all 12" reflected, that's a sweet t!ts paint job. Even 6" is still a mildly sugary t!ts paint job. 3" is more like sour t!ts. And 1" is like saggy, sour, wrinkledy old teats.
And if you don't want to pay to have car repainted properly, then the best you can do is use the SOFTEST car wax you can find. Wax and polish are used interchangeably with car waxes, so don't worry about that. But there are liquids, solids and spray ons. I would get a liquid wax. But whatever you get, DO NOT get an abrasive wax. That will ruin your old paint. Also, you need to be careful not to get the wax on any plastic parts. After that the only instruction is to take your time, apply the wax in the shade, or better yet, inside a garage, and take your time. The best shine will result from the most physical effort on your part. This will take most of an afternoon, if not all day. I dunno what you have in UK, but in USA, Mothers and 3M make pretty good auto waxes. Just read and follow the instructions on the bottle. GL! You won't get a "car show" finish, but your car will look better than it does now.