I've really only washed my car for the last couple of years. No wax, polish, clay etc, used to, but not anymore.
My white 93 325i is looking pretty dull & dirty.

Where should I begin?

Clean, clay, polish, then seal.

Clean the car with dawn, or diluted simple green. This will remove the dirt and old wax.

Claybar. Use a quick detailer as lubricant. Mother's and Meguire's systems are probably the easiest to find. (a wash after this step would be advisable)

Polish. I would assume you don't have a orbital buffer. But a Porter Cable random orbital buffer will make you life a lot easier. If you have a buffer, then a machine polish such as 3M's Finesse It Machine Polish would be great. Step up to a Fine Cut Rubbing compound where you have deeper scratches and swirls that you can feel. If you do not have a buffer, a swirl mark remover or a glaze is what you should use. They are not as strong as a machine polish, so you could be buffing by hand for a while before all swirls/oxidation are gone.

Seal. With a carnuba wax. Forum favorite is S100/P21S. Or seal with a sealant(synthetic) such as Klasse All in one, or Zaino. Or you can do both, seal with synthetic first, then wax over it.

Use microfiber towel to strive for perfection.

Is the compound the same as polishing?