I have a client who wants me to design a lettered graphic for the back side of his boat (18” x 72”)and he wants me to handle the printing-this includes finding the right printing material that can handle saltwater. So my question is, should I be the one handling the printing and finding the right material for it or should the client do this?
It all depends upon what you agree upon with the client.
There's nothing that states you can't find vendors to create the decal (or whatever).
It's up to you to decide if you want to find vendors. That typically means you deal with the vendor, pay for the product, and then pass on the cost to the client (with a markup).
If you don't wish to handle the production aspect, you are free to decline. Or at least explain to the client you don't/won't handle production. You will only create the artwork prepared for production.