As a woodturner, I do a lot of "sanding" (if I was a better turner, I would do less )
The modern abrasive sheets all outperform old style sand or garnet paper. Choose a good sharp grit, like the green sheets sold by Wickes etc. Good paper should cut, not wear down the surface.
Buy a selection of grits form 100 - 240. Use the finest grit that will remove the previous scratches, start with the coarsest and progressively go finer until you get the finish you require. DO NOT sand too fast (give the grit time to cut) or with much pressure, if you have to use any pressure, your abrasive is blunt and should be changed. On flat surfaces always use a sanding block to prevent hollows. On wood, sand with the grain.
If you are finishing natural wood with wax, try wire wool impregnated with wax.
Health and safety -- always use a mask (like what I do !!!!, when MrsP is watching or I am choking)
Bet you never knew there were sandpaper anoraks (all woodturners are)