Bathtub-Shower caulk advice

Our bathtub/shower is two pieces, the bottom half with the tub is one and walls for the top is another. Where those two pieces meet there is always mold building up in the crack between. I don't know if this is getting in the walls behind it but I do see some mold starting to form on the wall near this crack just outside of the shower... it may just be from the wet shower curtain touching it.

It is a good idea to caulk this gap all the way aroung the tub or will the caulk just cause water to gather there and make the caulk moldy?

Thanks,
Steve