Dejure is spot on. FYI, a wood door manufacturer insists that if all 6 sides of the door are not finished/sealed, the warranty is VOID. I also recommend an oil penetrating stain, then a marine spar varnish. Sikkens makes some great exterior wood products, hence their products price tag. If you really want a super-smooth finish, apply a good exterior sanding sealer(2 coats) after the stan, prior to the top coats(finish) of anything before hand, sanding lightly & wiping with a tack cloth afterwards. DO NOT OVER-SAND! I tell people 2 coats BEFORE sanding as it's easy to sand through a single coat, into the stained wood causing a splotchy appearance. Remember, that big orange ball in the sky WILL & DOES F U EVERYTHING eventually! My recommendation in steps below, if you want an almost furniture appearance & durability.
1) Lightly & evenly sand the wood first to smooth out rough grain & remove any light marks.
2) Apply a good oil penetrating stain, i.e., Minwax, Sherwin-Williams, with a rag or staining pad. Wipe off excess after about 30 seconds. Let dry 24 hrs.
3) Apply 2 coats of a good UV blocking sanding sealer, either with a brush or small roller. Let dry thoroughly. then sand lightly until smooth to the touch, wipe down with a tack cloth to remove sanding dust. This step is OPTIONAL
4) Apply 2 topcoats of your preferred finish/sealant with a good brush or short napped roller(1/4") lightly sand after dry, tack cloth, then apply one finish coat. A good oil-based Marine Spar varnish w/UV protection will probably hold up the best. Like Dejure says, you can also use a high-traffic Poly made for wood floors. Also, a semi-transparent or semi-solid oil stain will almost paint your wood and won't really allow the live grain to stand out, that's why I use a "penetrating" oil stain. Danish Oils & Tung Oil will look very nice, but they require almost continuos re-coating over the duration, and will gradually darken with each application.
PS: Lay stain rags out in the open to air dry, or burn right away! DO NOT throw them in a pile in the corner, garbage or ANYWHERE, as they WILL spontaneously combust! I am not sh*tting you!