I've had a cast iron tub refinished. When I checked the cost for another refinish ($700.00) it was cheaper to buy a new tub. I suspect you will find it will be cheaper to replace the tub rather than refinish it. If the tile floor is a color you dislike, you can tile over in most cases as long as the surface is sound. More than likely if you rip out the old tub, you will find dry rot in the floor and perhaps where the tub meets the walls. I've never worked with marble, but I assume it can be re-polished, however it may not be worth it. I just finished gutting everything in the bathroom to the studs, drywalling the walls, & re-tiling my whole bathroom using 2,000+plus tiles to do it. It seems one thing leads to another so plan it out. I had started by just replacing the faucet trim & see where it lead.