The best Tub & Shower caulk on the market " Polyseamseal tub and tile ultra"
In my opinion the best caulk on the market for your needs is Loctite Polyseamseal tub and tile ultra.
The problem with tub and shower caulks:
Although caulk appears to have a smooth surface it’s actually porous which gives mildew spores the perfect place to hide. Since most soaps and shampoos contain ingredients that mildew feed on, and water is always present, caulk can create ideal conditions for the growth and survival of mildew.
Loctites Polyseamseal tub and tile ultra caulk contains BioGuard™ an antimicrobial agent that helps prevent odor and stains caused by mold and mildew growth on the caulk surface, Silicone is added to increase durability and give a watertight seal.
To summarize, any caulk will mildew over time. The amount and quality of the antimicrobial agent in the caulk will determine how long it takes