Carbon yes, stress coat is only needed if the fish are exposed to cold temperatures or if the tank isn't cycled.
For the record, water isn't whats important when it comes to cycling a tank, its all to do with the filter media and the tanks substrate which holds all the beneficial bacteria.
You can buy a brand new tank and fill it up and have fish in it a few hours later if your using a cycled filter, doesn't mater if the water came out of the tap or an old tank, like i said its all about the filter and sometimes the substrate.
If the water is clear, not murky, doesn't smell off/stale then i would use it. (but still use carbon)
p.s "stella" they can't add too much more chlorine than they do allready as cholrine is poisonous.