Not even two years after I last caulked my showers and tubs, I'm faced
with doing it again, more for esthetic reasons than anything else - some
of the caulk has gotten pretty gross looking with mold or mildew,
despite the bathrooms being clean.

So I'm looking for a recommendation of an outstanding caulk for tubs and
showers. I guess my top criteria would be I don't want to be caulking
again in two more years, and I'd like it to be mildew-resistant (or able
to resist whatever the black gunk is that took it over).

Also, please give me some tips on applying the stuff so it looks good
and lasts long.

Pretty basic questions, sorry.