Stain of the type we're talking about here ("fence stain" or "fence life" products) if you use them are all you need to protect the wood as that's what their purpose is. Some are better than others of course but they're made to be the one and only thing you apply, many specifically calling for the wood to be clean and free of other coatings.
With the very strong, essentially solid, colour of modern exterior stains like this you're only a short step away from painting the wood and paint is actually the premier wood preservative, far superior to any transparent or lightly-coloured option. I didn't want to mention it earlier because you were set on the natural colour of the wood showing. But if you're willing to look into that option then I'd investigate natural linseed oil paint, milk paint and flour paint, all of which come with a promise of exceptional longevity.
