Sherwin Williams has a stripper that will remove 98%, or more, of the old finish the old finish. I would not start with sanding. But, sometimes I have to do some "spot" sanding after stripping.
The stripper is fairly easy to use, and it can be time consuming, and expensive on decks that have a lot of material, particularly ones with solid stain, and or paint.
I put up plastic where I don't want stripper to go, and spray it on with a pump garden sprayer. Wear rubber gloves and eye protection. This stripper is not like aircraft stripper, (it won't eat up alive), but it will get under you finger nails and burn after several hours of using it.
Apply a heavy wet coat on all surfaces and let sit. Ideally, you do this on a day where it is not hot and sunny. The stripper needs to stay wet, reapply as necessary. After a while, (hour or so?), you can use a long handled deck brush to scrub stubborn areas.
If your deck only has a thin film build up, that should do it. Then, you rinse with a garden hose. I use a pressure washer with a rotating nozzle, (it is much faster). If you have never used a pressure washer on wood, understand that you can fubar your deck with one, if your not very careful. A good distance must ALWAYS be maintained between the nozzle and the wood to prevent damage. With a rotating nozzle, always point the nozzle away when pulling the trigger, then move it toward the deck. If you don't have a rotating nozzle, use your widest fan nozzle. NEVER use a narrow, or pinpoint nozzle. You will raise some grain using a pressure washer, if you deck is not in good shape, or you get too close.
Slight grain raising is not a problem. Fuzzy wood is a problem. But, you can sand it back into shape if you need to.
On a deck with a lot of film, the stripping process can take all day, or more.
After stripping, you can apply a "brightener," SW's is called Revive. This will lighten the dark, water blackened, boards and remove any black mold. This product works fast, almost before your eyes. Apply to wet deck wait a few minutes and rinse.
After the wood dries, (1-2 days), sand as necessary to remove stubborn areas, or smooth grain. Avoid sanding fasteners.
Applying an oil based toner: After the deck is completely dry, spray on wet, with a pump sprayer, allow 5 10 minutes to saturate. After finishing an area, use rags to sop up any puddles. Puddles that are allowed to dry, will not harden properly. Second coat is optional, After the first coat is mostly dry or more. I usually do a second coat. The second coat will take less material, Make sure you wipe up the puddles again, when finished.
You could probably get away with a water based product on newer wood, I always use oil based toner.