Start with a good clean, claying is easy and safe as long as you don't do anything strange. Clay mitts are much easier to use and can be reused many times although I think clay bars are slightly more effective.
As for machine polishing, it is always worth looking on Detailingworld, lots of great information on the various options. Essentially these days there are standard machines which are very versatile, there are longer throw machines which seem to work much faster and have less vibrations but are limited in terms of pad sizes however I have not tried any of these machine. There are variations which are very popular with the professionals such as the Flex 3401 as they have greater power but these are not cheap. Final option is a rotary, these have a terrible reputation for damaging paint very easily and taking years to master. Neither is completely true. A rotary is much faster and can cause damage if the operator is careless but the same could be said for any power tool. A normal DA polisher is almost plug and play but a rotary does take longer to learn.
Working on older paints can be very
satisfying, one product which is always worth considering is the Meguiars No7 glaze. It is a non abrasive cleaner which seems to hydrate older paints. This is a very long thread but worth reading at least the first few pages The Secret to Removing Oxidation and Restoring a Show Car Finish to Antique Single Stage Paints
Even if you intend to polish by hand or machine, the No7 is worth using before hand. You can use many modern products on older paint just make sure they are not very harsh. I think No7 has been around since the 1920's or 30's but it still works very well on older paints.
If you do intend to machine polish the paint, be aware, the pads will quickly turn the colour of the paint, this is normal. The trick is to keep cleaning the pads and the cleaning also applies to working on modern cars. If budget allows, get at least two of each type of pad eg compound and polishing, the process will be much easier. A pad loaded up with old polish will not work effectively and may introduce new swirls into the paint plus the pad will start to overheat which can easily lead to the pad failing whilst polishing - not a good thing.
Might have gone into too much information here but I do envy you, older paints really can be very satisfying to work on. Just remember older paint is not as tough as modern stuff so avoid any really harsh products and enjoy yourself