Get some 15W40 Rotella or other brand (dino) diesel oil and run it, even after break-in it's better for old school flat tappets than modern EPA oils.
My son has a '70 Mark III with 128,000 on odometer we've been doing some tinkering on
New motor, trans, suspension, exhaust, radiator, brakes, AC, rear end... and he just got 20" wheels on it today
As for the paint, Meguiar's has several products for buffing/polishing, just make sure you use a low speed buffer and go easy until you can see how much you're taking off so you don't get down to the undercoat (been there, done that) If you're not comfortable, get an estimate from a local paint shop, it's not worth ruining a good original paint job to save a few bucks (especially when you factor in the cost of a new paint job)
Oh, not to be difficult but, there's no such thing as a 68 Mark III (I'm assuming that's what you're working on) or a 68-1/2, they were all designated by Ford as 69's despite the early start to production.