How should sandpapers of different grits be matched with the hardness and elasticity of the polishing discs to optimize the surface finish?

Coarse sandpaper (like 40-120 grit)
Polishing pad hardness: You should pick a harder polishing pad, like a metal one or a hard rubber one. 'Cause coarse sandpaper has a strong grinding power and it needs a harder pad to support it to make sure it's stable in the grinding process.
Polishing pad elasticity: The elasticity can be a bit less. Coarse sandpaper is mainly used to get rid of big flaws and old coatings, so the need for elasticity isn't that high.

Medium sandpaper (like 200-400 grit)
Polishing pad hardness: You can choose a medium-hardness polishing pad, like a softer rubber one. This kind of pad can give some support and also fit the grinding power of medium sandpaper.
Polishing pad elasticity: The elasticity should be medium to make sure when you're removing smaller flaws and grinding the coatings, you can apply force evenly on the surface of the workpiece.

Fine sandpaper (like 600-1200 grit)
Polishing pad hardness: Choose a softer polishing pad, like a soft rubber one or a sponge one. Fine sandpaper has a weaker grinding power and it needs a softer pad to avoid damaging the surface of the workpiece.
Polishing pad elasticity: The elasticity should be larger so that in the process of fine grinding and polishing, it can better fit the tiny bumps and dips on the surface of the workpiece and get a higher smoothness.

Extra-fine sandpaper (like 1500-3000 grit and above)
Polishing pad hardness: A really soft polishing pad, like an ultra-fine fiber one or a specially made sponge one. Extra-fine sandpaper is mainly used for fine processing and mirror polishing, and it needs a really soft pad to avoid scratching the surface.
Polishing pad elasticity: The elasticity should be very high to make sure it can stick closely to the surface of the workpiece during polishing, and spread the grinding power of the extra-fine sandpaper evenly to every corner to get a very high smoothness.