Conventional approach (and it certainly works well for most jaspers, agates, feldspars, obsidian, etc) is to use two hard (diamond in metal) wheels (80-120 range, and 180-220 range), followed by series of soft wheels (changeable silicon carbide or diamond belts on expanding drums, or permanent soft wheels such as Nova). Example soft-wheel series would be 240, 600, 1200, 3000.
The mechanics of abrasive action are quite different between the hard and soft wheels, so it turns out that stepping back to rougher grit (100-180 range) on the first soft wheel after rough shaping on the second hard wheel often saves time, especially for harder stones.
While it's fun to learn and compare Mohs scale hardness values for various minerals, such "scratch hardness" of large, single crystals is not always related to the more important and practical grinding hardness of lapidary materials. You will quickly learn that one kind of jasper may wear down at double the rate of another kind. This is due to different microstructure of crystal grains, trace impurities, etc.
When you get to polishing, you will find online charts suggesting best combination of the disc material (felt, leather, canvas, synthetics) and polishing compounds (alumina, cerium oxide, diamond, chromium oxide, tin oxide) for a given stone. Unfortunately, these charts omit other, equally important, details such as pressure and time, and how wet the disc is... Old books and magazines, and forums like this one, are full of sometimes contradicting advice about polishing techniques. Use them as a starting point, but the key is to experiment and to keep your notes.
Be mindful of cross-contamination. Water mist generated by the wheels carries rock dust with it. Do not keep that polishing disc on the shaft - only put it on when you are ready to polish, and store it in its bag or box when not in use.
Also, be mindful of the danger of silicosis. Freshly fractured crystalline silica is quite reactive, and fine, invisible dust can travel deep into lungs where it leads to chronic inflammation. Always grind wet. Water keeps the dust down, but some research also suggests that it may help neutralize some of the surface reactivity of quartz. Still, an appropriate respirator or a mask, rated for water mist and sub-micron particles, is a good idea.
Good lighting is important when grinding/polishing, but also when inspecting the stone between the grit steps.