According to :

Removing shower/bath caulk is not a job I ever want to do again. It is
just nasty, annoying and frustrating. Or at least it was for me...
before I did it, I kept reading about how once you get the caulk line
started, it just pulls right up.

It depends entirely on the substrate. A few weeks ago I pulled
a line off a shower joint. Relatively new, it was practically
falling off. The shower wasn't properly cleaned first. Others
are much nastier.

Oft times, if you simply manage to shave out the worst/thickest of a
stubborn caulk line, recaulking over the remaining film is perfectly
okay. If it's not coming up, it's not gonna leak there either.

2) What is the best caulk to use? Silicone? Siliconized latex? I had
a mold and mildew on the old caulk and want something more durable.

I used that GE Silicone II stuff. I don't know if it's the best or
not, but there was some reason why I chose it, and I think part of it
was the advertised mold resistance.

"Bath and tile" caulk has stuff in it to kill mould. GE Silicone II
comes both with and without the mildewcide. Check the label.
--
Chris Lewis, Una confibula non set est
It's not just anyone who gets a Starship Cruiser class named after them.