Questions a bit vague but here's some:
Start with pH, Total Dissolved Solids (TDS), Total Suspended Solids, Total Organic Carbon (TOC) and Chemical Oxygen Demand (COD).
These are basic tests. They absolutely will not assure you of suitability to your application. OTOH, if any of these are "bad" (whatever that means), you almost surely have a problem.
Think, necessary but not sufficient.