Two systems, not two options
Czechia has a public health insurance system and a market of commercial policies for foreigners. Which applies to you is not a preference - it follows from your situation.
You are in the public system if you are employed by a Czech employer, if you hold permanent residence, or - since 1 January 2024 - if you are a child under 18 with long-term residence. In those cases commercial insurance for foreigners is money spent on something you already have.
You need commercial cover if none of that applies: typically non-EU nationals staying over 90 days who run a business or do not work here at all.
Where it gets confusing
Self-employment is the usual trap. A trade licence looks like work, but unlike employment it does not put you into the public system. People who switch from an employment contract to their own business sometimes discover this only when they need a doctor.
The other frequent moment is losing a job. Participation ends with the employment, and a gap in cover causes trouble both medically and when the immigration authorities ask for proof.
What to check before you buy
If you do need a commercial policy, look past the price at the scope: what care is covered, what the limits are, whether there is a waiting period and what is excluded. For a residence application, comprehensive cover is generally what is expected - verify the specific requirement with the Ministry of the Interior or the embassy where you apply.