The sanding operation creates heat so any dirt, grease or wax will be cooked into the wood and may cause adhesion and drying problems when finishing. Clean and then rinse with fresh water several times. If the floor has been waxed, use a stripper following label instructions, rinse well and allow to dry thoroughly. Do NOT use TSP on bare wood, as it may badly discolor the wood's natural tone. Cracks Wood floors need cracks, so avoid too much filling.
Old floors have charm, which includes a few gaps and holes.
Starting with 36 then going to 20 gives a better bite for the coarser paper and is more effective. The old finish is probably hard and quite smooth. Sanding gives a good mechanical bond for the new finish. For NEW floors, start with 60 grit and finish with the 80 grit sandpaper. This leaves less clean up later and lets you see your work area.