Congratulations to you! ✨
My husband and me prefer private and we went ahead with it.
I would say it depends on what is your priority?
You have to see your comfort level and financial capabilities because there will be a lot of commitments ongoing. Some mommies priority is gynae’s choice (if you have any gynae in mind you would like him/her to assist you) and/or hospital. You can consider going for hospital tour too.