Metals in pool turn water green after adding shock, what's the solution?
There are several independent variables to manage in a swimming pool or hot tub:


pH balance
halogen balance
calcium hardness
total dissolved solids


Nearly everyone is aware of pH balance, but what most people don't seem to understand is that pH can swing wildly unless total alkalinity is increased sufficiently to provide an "inertial buffer" with total acid.  Then moderate changes in chlorine or bromine content do not affect the pH so much.

The other thing most people are familiar with is chlorine.  Bromine can be used instead and is just as effective at killing bacteria but with possibly less skin and eye irritation.  At my pool store, they are priced the same.  The standard home pool test kit measures both pH and "free chlorine equivalent".

Calcium should be added to soft water to prevent the water from attacking and rusting metal components of the pool and filter system.  This is a particular problem for areas such as the Pacific Northwest which has naturally soft water.  Most well-based systems will have some calcium, but if it is not adequate, some supplementation is cheap insurance for minimal maintenance.

See this for a detailed and reasonably approachable roundup of pool chemistry.  Note that everything affects everything else, so reading it twice is probably necessary to gain full insight.

In my experience, green water could be caused by either iron or copper in the water, like someone's lost jeans rivet inside the drain.  A chemical to precipitate and flocculate the metals need be done only when it is a problem.

If the history of the water is uncertain or a lot of junk has entered the pool water since it was last filled, there is no substitute for draining and refilling it.  This reduces the total chemical load to the minimum and will make it simple to balance.  To maintain that simplicity, insist that all pool users shower before entering to remove sunscreen, oils, perfumes, deodorants, etc.