If your getting blue stains, this usually means a low PH and it's slowly eating your copper plumbing. A water softener will not cure this problem unless they put some calcite in the tank with the softener media. I don't recommend this method as the calcite is sacrificial and when you need to add more, you have to disassemble your softener to do so.
I would first get my PH checked along with the hardness, iron and anything else you think might be in your water. If your on a well, you might want to get some other tests as a low PH can mean surface water.