Those pipes served that home well, probably for nearly 100-years or more. It's probably time to replace them. These things are HEAVY, and can injure you or damage the building if they fall. So, some would consider having a pro to do this. It is doable if you are careful.
A saw to cut the stuff is slow and a pain. Better to rent a cast iron chain cutter. This wraps around the pipe, you tighten it up, and it cracks the pipe. Yours may crush, but the end result will be the same, you will have made a break in the pipe. Wear gloves, safety glasses, and long sleeves in case a shard decides to jump out at you. Where the pipe goes through a floor or ceiling, ensure it is supported so it won't fall - there are special clamps designed to do this.
Both PVC and cast iron will last a long time. The cast iron will be quieter but harder to install. If allowed in your area, they also make a foam core pvc that is supposed to be a little quieter (and lighter). It is NOT as strong, so that might also be a consideration. Most places just use the solid stuff. Maybe one of the pros will comment.
If the drain lines out to the sewer are cast iron, they could be in fine shape, or similar to the stuff in the house. Hard to tell without a good inspection.
Last thing I can think of, there's probably a lot more. What you have probably doesn't match current codes and practices, so you probably shouldn't just copy what is there; you'll need to get some advice to get it right. Come back with questions as you have them...