These plans meet all the requirements of the health care law, including covering pre-existing conditions, providing free preventive care, and not capping annual benefits. If you have one of these plans, you won’t have to pay the fee that people without coverage must pay through the 2018 plan year. (Note: Starting with the 2019 plan year (for which you’ll file taxes in April 2020), the fee no longer applies.)
A good place to start is HealthCare.gov. This is the health insurance exchange created by the The Patient Protection and Affordable Care Act, and is a one-stop shop for private individual market health insurance plans (note that the exchange itself is run by the government, but the health plans for sale in the exchange are all private, from the health insurance companies with which you're already familiar). People in 39 states use HealthCare.gov to enroll in individual market plans. The other 11 states and the District of Columbia have state-run exchanges, and you'll be directed to their sites from HealthCare.gov when you select your state.