Sand and prime with CoverStain, topcoat with a high quality satin exterior paint or semi gloss if you like it more shiny. Those thresholds are always maintenance issues though because people step there and then push off when they enter and leave the home...impossible to keep paint stuck forever. I usually repaint mine every 2 years.

If you're going to paint it, be sure to glue the splinter down, feather sand the edges, prime, paint.

Above advice=EXCELLENT!

I'll only add, that if you want to see the wood-grain, consider using an Exterior SPAR High-gloss OIL (S/G minimum...) Poly/Varnish. 4 coats now.
Then you'll just have to do a maintenance-coat or 2 every 2-3 years.

Faron