Beautiful bikes, and totally deserving of some love. Did you see that era of Specialized MTN bikes getting some retro-love at Unbound Gravel this year?
https://www.gravelcyclist.com/bicycl...lized-diverge/
Veterans and experts can pick the right level of aggressiveness and work their way down to a pretty finish. The rest of us need to work our way up, from gentle to more aggressive and then back down, and bikes are harder than cars because the decals are not all equally protected by the clearcoat. I think most vintage bike people in the US seem to be working with Meguiar's products, but your local auto parts store will be happy to show you the safest order of attack. Anything called a "compound" or "polish" should work by gently grinding into the surface of the paint, so work slow and excercise care around decals. Surface treatments like waxes or silicone finishes work by filling in the gaps, and really can work wonders on old paint without the danger of rubbing something away. Good luck with those great looking bikes.