What you have on it will determine how you clean it. No stain at all and only grey lignin (wood fibers)- then use an oxygenated bleach (not sodium hypoclorite- which is house bleach)... it's a percabonate cleaner
From what I can tell though you have an oil based stain on their now. Oil based stains (most of them) will break down on a molecular level using a caustic like sodium hydroxide or potassium hydroxide. .. do NOT use a gel, soy or varnish stripper or anything with methlyen chloride. . Way too caustic.
Your going to want to apply the striiper heavier on areas with stain, lighter on bare wood. Let dwell and keep agent active by misting it. You'll know it's working when you see it wiping off with your finger. Power wash the deck with a white (40 degree) tip. Do not exceed 1200 psi.
There are two side effects with stripper and high psi.. one is furring (caused by two much pressure) .. the other is fuzzing (raised grain due to the lignin breaking down that holds the wood fibers together)...furring is damage. Fuzzing can be fixed with light buffing/sanding.
Wash the outside spindles, inside spindles and then floor last. Hold wand away from deck, pull handle and feather it into the wood. Walk the entire board out and feather it bwck out at the end. Do not start/stop/start/stop etc as this will cause pressure lap marks that will bleed through the stain.
Once done you will need to neutralize the deck if you are going with an oil base stain. Oil based stains "prefer" acidic surfaces. Use either citric or oxilic acid. The consumer brand sold as "brightner" @ your local box store should suffice. I mix my own from raw powder but I do a lot of decks
The brightner will swing the pH Back in line to accept an oil.
Let the deck dry for at least two da6s...I use a moisture meter and less than 12% is ideal.
If you Have any fuzzies, I've found green kitchen scrubbies sold in the paint section of menards work grear. Or you could use a palm orbital sander with 120 grit or an Osborn brush.
Product choice is up to you but like other's have mentioned stay with a true penetrating oil. Your deepest penetrators will be parafinic oil based stains like ready seal, armstrong clark and ABR (long oils)... other types are linseed and tung. Keep in mind linseed is full of starches and can be a natural food source for mold and mildew. I live in a "green state" and oil stains are getting harder and harder to come by. Personally I've had good luck with Floods UV-5 oil with Penetrol. It applies nice, penetrates pretty good and is easy to strip down the road.
Stay away from acrylics. I could go into all the reasons why but just take my word for it. Also some oil based stains still have a percentage of topical membrane properties and can be tough to strip... Like behr, Cabot and sikkens.
I forgot to add, stains like ready seal work best only if you can remove at least 90% of the old stain. So if there is a lot of residual stain left after stripping you will need to sand.
If you do like the solid look or want a two tone deck like someone mentioned don't go with a 100% latex. Stick with one of the hybrid solids that have an alklyd and waterborne polymer. They are sometimes referred to as self priming stains. Again o use Floods SWF in those cases but there are other good brands.
Hope this helps. I'm still learning the flooring trade but decks and exterior wood is my forte.
GL