HOW TO PAINT AN OLD RADIATOR
You must remove all existing rust. For this you will need gardening gloves and wire wool. If it is very bad you can use a wire brush. If it is very bad and the welded seam is rusty, take it to the tip as it will leak. The bottom is usually worst, and the end joints. There may be rust on the back which is very unlikely ever to have been properly painted.
You cannot do it adequately when it is hung on the wall. Use fine wet-and-dry abrasive paper to remove old blobs and runs of paint and to raise the shine off. 600 grade, wet with water, is suitable.
When all the rust is gone, use an anti-rust chemical. I recommend Kurust which also primes the surface. You can get it from motorists shops or online. Do not drink it or put it on your skin or eyes.
Then, use a metal preservative primer for ferrous metal. It is surprisingly expensive and heavy, but a 250ml can should be all you need. Apply very thinly to all exposed metal. Two thin coats are better than one thick, you may need to thin it, usually with white spirit, in a small glass jar.
I don't use an undercoat, because the thicker the layer of paint, the more likely it is to crack or craze from heat expansion of the metal
I recommend a matt or eggshell type paint. You can paint it to match or tone with your walls. Radiators do not have to be white unless you want it.
Emulsion paint tends to soften from heat when new, causing dirt and dust to stick to it and be unremovable.
Paint the ends first, then the top and bottom, then the back, then the front last. This is to minimise the risk of marking the front while you're working.
When you refit the radiator, you need little plastic horseshoe washers in the wall bracket slots, which allow the radiator brackets to slide as they expand without clicking or creaking. These are often forgotten.