How do you choose a public vs. private (invite only) community

I am in the process of building a community targeted towards Product Managers. The goal is to create a space where PMs can share ideas, problems, jobs, etc with other like minded people.

I have decided to go ahead with Discourse to build the community, and it is live as of today. I strong believe that the quality of initial users / adopters of the community define how good and valuable the community turns out to be. With that in mind, the questions are:

How do I ensure quality of initial users is very high?
On the same vein, should I limit access to the community and make it private or invite only?
If I were to limit initial access to ensure high quality, what are the things I should keep in mind while recruiting the initial set of users?
Any insight into how IH got its first set of users? And why IHers even today are such a highly motivated class of inidividuals?
Since I am only starting out, and there is no credbility of the community yet, I believe creating a paid option is not a good direction to take.

Also, open to hear ideas on how I can make this community unique and attractive to Product Managers. There are a lot of PM communities, but none of them are as strong as I would hope. And, I am unable to think of why that is, or how I can change that