When can I get healthcare?
The K-1 visa is a non-immigrant visa so you should be covered under travel insurance until you get married and apply for Adjustment of Status.
You can get healthcare using the marketplace from Healthcare.gov, however you can only use the Government marketplace after you apply for Adjustment of Status to LPR.
Or you may be eligible for Medicaid if you come from a low income family (in the USA, basically your fiancé/wife).
If you don't have minimal health insurance in the USA you may have to pay a fee. The minimum essential cover is:
The type of coverage an individual needs to have to meet the
individual responsibility requirement under the Affordable Care Act.
This includes individual market policies, job-based coverage,
Medicare, Medicaid, CHIP, TRICARE and certain other coverage.
As per the paper application for HealthCare.gov:
Before you begin, it may help to have this information ready:
Social Security numbers (SSNs)
Document numbers for eligible immigrants who want health coverage
Paystubs, W-2 forms, or other information about your family’s income
Policy/member numbers for any current health coverage
Information about any health coverage from a job that’s available to you or your family