My first ever piano arrived last week. Its a 1976 Yamaha U3.
The whole family loves it and there's a bit of a queue to use it

Anyway, there were some superficial scratches on the surface which under certain visual angles are exaggerated. This bothered a bit so after a lot of research, I read that certain non-agressive polishes might do the job.
Off I went to our local hardware store (Bunnings) and bought the least abrasive polish i could find. Enter Turtle Wax Scratch N Swirl Remover. At $10 for a small bottle, it wasnt cheap but I tried it anyway.
Armed with a good micro fibre cloth and gentle force, I was able to work this polish around the areas with the light scratches. Some scratches which were a little deeper needed more forceful rubbing.
After using the turtlewax, i polished the surface to a glossy shire and to remove all traces of it. Then I used Meguiars Kwik Detailing spray which gave an even glossier shine.
I am happy with the result overall as the light superficial scratches have disappeared. The deeper scratches that you can actually feel with your fingers appear to have lessened. I think the turtlewax filled in the grooves somewhat and the spray afterwards blended it well.
The only issue I have with the Detailing Spray is that dust and fingerprints appear to be attracted to it. I am now thinking of buying the Cory product that is quite popular on the piano forums...