If it were me, I would use a coating that's called "Marine Varnish" by
some people, and "Spar" Varnish" by others. You should be able to buy
it in any paint store, but any marinas in your area will certainly carry
Marine/Spar varnish is similar to an alkyd based polyurethane, but it
doesn't dry as hard and is very much more naturally resistant to UV
light from the Sun.
You can buy alkyd based polyurethanes that have lots of UV blockers in
them for use outdoors as well, but I don't know about their hardness.
With hardness comes rigidity, and wood is a natural material that swells
and shrinks with changes in it's moisture content caused by seasonal
changes in temperature and humidity. So, if it were me, I'd use a
product that's naturally UV resistant and and dries softer than regular
interior polyurethane SO THAT it retains enough elasticity to stretch
and shrink with wood outdoors.
I looked at your picture.
If it wuz me, I would use a paint stripper like PolyStrippa to remove
what's left of the peeling coating on your exterior doors. I suspect
the coating is peeling because someone used an interior oil based
coating on that wood, and the coating isn't soft enough to stretch and
shrink with your wood. Then, if those orangy stains come off with the
coating, you might only have to sand those black stains out.
You then need to get a wood stain mixed up at any paint store to match
the stain you have now, and use that to restain your THRESHOLD (not
"bottom floorboard") and any areas where you sanded the stain off the
same colour as what you have now.
Then apply multiple coats of Spar/Marine varnish.
I'd also ask at the paint store or marina where you buy the spar varnish
whether they have a "wiping" marine varnish. Wiping "varnishes" or
"polyurethanes" are made with much smaller resins than regular "brush
on" varnishes or polyurethanes, and that means that they're not nearly
as viscous as regular varnishes or polyurethanes. The advantage to that
is that they won't leave brush strokes on your wood even if you paint
them on with a corn broom. They're meant to be applied to a dry rag and
wiped onto the wood surfaces being varnished.
(Keep your wiping rag in a plastic bag to slow the rate at which the
wiping spar varnish cures with the oxygen in the air to form a solid.
No matter what you do, the spar varnish will absorb oxygen as long as
the rag is exposed to the air, and that oxygen will cause the spar
varnish to solidify even when the rag is wrapped in plastic. But,
wrapping it in plastic will at least allow you to use the same rag 3 or
4 times, rather than just once. Use a clean WHITE rag as any dyed
cotton rags could discolour your varnish.)