Decision Making: private or statutory health insurance?

Hi fellow humans!

I'm moving to Berlin, Germany, a few months later and was prompted by the relocation company to consider health insurance. They offered to get me in touch with TK or Barmer if I want to go statutory. For private, the agency referred to something with enough coverage, like Hallesche private insurance.

More about me: I have a generally healthy lifestyle and haven't faced many issues. I have no children and am 31 years old male. Things I seek medical assistance for are:

a) mental health (medicines and therapy): currently doing both in the NL covered by my insurance
b) occasional cold / flu.
c) Ah, also, I wear glasses/contact lenses
d) I prefer having regular dental check-ups since I had a root canal 3-4 years back, and eating food before was a painful experience. I am a bit more cautious about my teeth now because of my love of food.

Since I live in the Netherlands, I'm confused about how insurance in Germany works and which ones I select for my particular case. Also, if there are any websites to compare private vs. public and the service providers within each segment, that'd be helpful.

Danke!