The widest range of stones to choose from. Coarser stones are best for fast, flat edge setting and geometry repair, medium for standard maintenance edge setting and fine for finish work. Always follow up on a strop with chromium oxide to remove burr.
As a general rule of thumb for most maintenance sharpening on dull edges, start with a coarse stone -- 400 to 800 -- to re-set flat edges and bring the two bevels into contact to form a burr quickly and cleanly, within 5 minutes. Often working for too long on this first stage with a medium stone makes for a rounded edge.
Keep in mind not all knives benefit from the finest polish possible. Steel type and type of use determines the optimum finishing stone. A slicer made from shirogami can benefit from an high 8000 grit finish, while a santoku made from aogami does not. Often lower grit ‘toothy’ finish stones -- 2000 to 4000 -- will give more bite which can translate to longer edge life on stainless steels, whereas fine finishes (5000 and up) have a more razor like keenness but can make stainless steels slippery.
Having several stones to be able to choose the right finish for variety of knives is ideal. Having several stones also allows for a variety of finishes by sharpening each side at a different finish. Ex 8000 on inside bevel, 1000 on outside….
Some natural stones are great with Japanese double bevel knives. Generally, the more complex the alloy, softer, slightly coarser stones are best (LV 3-3.5 in hardness and fineness) often very hard (LV4 to 5) stones will make scratches in hard high alloy steel.
Diamond stone flatteners are best to quickly level out the widest range of stone grits. Some flatteners can leave behind large particulates on finer stones that can leave deep, unexpected scratches. Use your fingers to feel for any malignant grit that needs to be cleaned off. After flattening fine stones, use a nagura or second fine stone to smooth out the grooves left from the flattener.