Ive attached photos

I'd go to a true Value Hardware store and talk to the paint department about Woodsman or Zar stain. This is a common problem. They can explain the step by step process to prep and stain your deck.

Im partial to True Value, but any quality hardware or paint store can help guide you.

You need to get every bit of that paint off before any other finish is put over it. I would look into new deck boards over the existing framing.

Yes millworkerman is correct, all paint needs to stripped before stain will absorb. Some new products do make it a lot easier and cheaper than previous to do this.

The wood still in fairly good condition, no cracks, etc the surface needs to be properly prepped as mentioned here and apply the desired finish.

Good luck