You must have an HDHP if you want to open an HSA. Sometimes referred to as a ‘catastrophic’ health insurance plan, an HDHP is an inexpensive health insurance plan that generally doesn’t pay for the first several thousand dollars of health care expenses (i.e., your ‘deductible’) but will generally cover you after that. Of course, your HSA is available to help you pay for the expenses your plan does not cover. For 2019, the minimum deductibles to qualify are $1,350 (self-only coverage) and $2,700 (family coverage).
The annual out-of-pocket (including deductibles and co-pays) for 2019 cannot exceed $6,750 (self-only coverage) or $13,500 (family coverage). HDHPs can have first dollar coverage (no deductible) for preventive care and apply higher out-of-pocket limits (and co pays & coinsurance) for non-network services.