Bob, if the tub has a cold metallic feel its cast, if it feels light and plastic like, its fiberglass or acrylic. Generally, it's considered best practice to set fiberglass/acrylic tubs in a bed mortar so the base is fully supported. They also need to be properly attached to the walls. Low bid contractors don't always bother with the extra step of the mortar, nor correcting out of square walls so you get a nice fitting tub/tub surround.
Almost all caulks flex, its just a matter of how much and under what conditions. 100% silicone is the best, assuming you don't have a really big gap. If we're talking 3/8" or less then silicone is good. If the gap is 1/4" or bigger then you'll want to use backer rod. The backer rod does two things, first it backs up/gives the caulk something to stop it from pushing all the way into a big gap. Second thing is it gives the caulk the best shape/form for flex and adhesion. The shape is sort of like an hour glass, wider on the ends for adhesion and thinner in the middle so it can flex without pulling itself off what it is adhered to. Sizing the the backer rod correctly is also fairly important for the ideal caulk joint. The backer should compress only enough to hold in place. You don't want to jam a 1/2" backer in a 1/4" gap since it will reduce or eliminate the chance of the perfect hour glass shape for the caulk. Check out this image to get an idea of what I mean.
