Is private health insurance necessary?
No, not if youre an EU national. A EHIC (European Heath Insurance Card) should cut it.
How much does it cost and what does it cover?
Depends on the insurer
Is it cheaper to just pay out of pocket if you are sick?
That depends if you want to wait in a cue or not and what the medical issue is..
I've heard very mixed reviews about the public hospitals and clinics that are free.
You'll never get decent specialised care in a private hospital in Poland out side of Warsaw