Really will depend on what is wrong with the finish in the first place... severe swirls? light swirls? paint fading?
If its paint fading, my first port of call would be a chemical cleanser such as Klasse AIO applied by PC.
If its swirls and marring thats the problem, then looks at abrasive polishes - I personally like the Menzerna and Meguiars ranges, but with the correct techniques of application, the vast majority of polishes out there will deliver excellent results. Proceed with care on old paint, you never know what its previous treatment has been, and start with a mild abrasive first on a test spot and work up the abrasive scale until you reach a polish and pad combo that delivers the required results before doing the whole car.
