Dude, forget that mess, and just get it reglazed. Its a fraction of the cost as a new one, and looks brand new when done.
If you do decide to pull it out, go with the sledge hammer, and wear safety goggles. (myself, I wear safety goggles 24 / 7, no matter where I go. Never can be to careful) you'll need to tear your existing surround or tile down, and replace with green board, or ideally, Durock. Be prepared to do some framing also, as you will most likely have to make some modifications to get the new fiberglass tub in, even if the advertised dimensions are the same as the old. And, if you have a cast iron tub, I'm sure you have a least some cast iron plumbing. You'll probably end up tearing some of your floor up too. If you have a few skills, and a BFH (big f***king hammer) you can do it. But I would seriously look at reglazing it. Heck, it might even work out better for you just to fly me down there and let me do the work in exchange for beer and an erotic massage.