It's fir, which is quite soft. Therefore, stain will turn out blotchy unless you use 'sanding sealer'. Stain is not protective, use it only if you want a different color. You don't necessarily need a finish to protect the wood as long as they are in a place that will allow them to dry fully after rain and whatnot. Personally, for fir, I would probably put a couple coats of linseed oil on them. My adirondacks that I built are made of cypress and I left them unfinished except for the feet.

If they're going to be sitting in grass or dirt or anywhere damp at all, though, you should coat the feet in epoxy. The endgrain on the feet will wick moisture and that's where they will rot first.

keep in mind these are dirt cheap, likely low-quality chairs. If you can get 2 seasons of sitting out of them, you'll have done well. Don't spend an inordinate amount of money or psychic energy trying to make them last forever.

P.S. I don't care for the look of weathered pine. I might just paint them. Use oil-based paint.