Water filtration system recommendations
A 5-stage reverse osmosis / UV filter will likely give you the results you want.  This will filter out heavy metals as well as viruses and bacteria.

Downsides:


Cost (~$400, plus consumables)
Maintenance (new filters every 3-6 months, new UV lamps / membranes periodically)
Waste water (Every gallon of purified water produces at least 3 gallons of waste water)


After installing, I would definitely send a sample of the filtered water off to a lab to verify that it is potable.