What are the advantages of various bathtub materials?
Cast iron tubs are very heavy and expensive.  Rust is not a problem with cast iron tubs as long as the enamel top layer is intact (if you get a chip in it, you can get enamel repair kits).  My wife did not like the old cast iron tub in our bathroom because it was cold when standing in it during a shower and made bath water get cold fast.  Evidently she was not taking baths in the “cast iron method” which is to put super-hot water into the bathtub and allow the heat to transfer into the tub, this will cool the water down but keep it at a reasonable temperature longer (in theory at least, YMMV).

Enameled steel it basically a cheaper version of the cast iron, it is a lighter because the metal is much thinner. I doubt the “hot bath trick” described above for cast iron tubs will work in a steel tub.  Like cast iron tubs, you should not have to worry about a steel tub rusting or cracking.

Acrylic (plastic) tubs come in a different quality levels.  Some are really cheap, thin plastic that have the potential to crack over time (particularly if they are poorly supported/improperly installed).  However some acrylic tubs use thicker stronger plastic (often with fiber glass embedded for tensile strength) that are very sturdy.

I recently had to make this decision; we replaced our cast iron tub with plastic Kohler model.  I knew I did not want to lug a cast iron tub up to the 2nd story.  I thought about a steel tub but they are still 120-150 pounds.  I was worried about getting a cheap plastic one that would break so I settled on a $700 plastic Kohler tub that is pretty thick.