Sampling guidelines have changed over the years - fifteen years ago it was normal to test the water only for bacteria (potability). If no bacteria was found in the sample it was considered "drinkable" and of no further concern.
Today's standards are different as people become more cognizant of multiple environmental hazards and pollutants that can affect drinking water. In this area, while rare, well water samples have tested positive for arsenic, uranium, and other contaminants.
I recommend, at a minimum, that you have the water tested for the following before drinking:
- Radon in Water
- Lead (can come from older water supply pipes in the home)
- Volatile Organic Compounds (if there is / was any question of a buried oil tank near the home)
Of lesser health concern, but important from a functional standpoint, would be testing for the following contaminants:
- Nitrates and Nitrites
- Color, Odor, Turbidity
The State of Connecticut Department of Public Health has published a guide for testing your well water that should be reviewed by homeowners with a well.