Truly Personal preference. My thinking was copper offers more rigidity so being on an utility sink and connected to the washing machine to me felt best choice to avoid any issues if you move anything or bump it using the utility sink.
I'm replumbing an old utility sink. I have to ask why are there no shutoffs on the supplies going to the faucets? I see yours is like that too. I get there are shutoffs on the washer supply lines, but it seems like they would be helpful above the faucets also.
It's not a bad idea to put valves in. But utility sinks like this tend to be piped directly instead of having supply lines like a normal faucet or a washer.
I'm a little confused on the question. Are you sure it's cast iron or could it be galvanized pipe? If it's galvanized pipe and threaded I would recommend hiring someone. Galvanized pipe is threaded and could break or cause another fitting to leak causing a bigger problem.
