Facebook Personal Page vs Facebook Business Page

Hi Coach, I am starting my coaching business and am learning more about social media. I have a personal Facebook page that I rarely ever post on.

My question is:
1) Do I create a new Biz Facebook page for my coaching business and have no reference from my personal page to it?
2) Do I create a new Biz Facebook page and create a post about this on my personal page?
3) Do I convert my personal page to biz page?

If I had to choose today, I would create a Biz FB page and mention it on my personal page. This feels appropriate and from abundance, not lack. I know the people on my personal page and believe they would want to be aware that I have started a coaching business. Converting my personal page to a biz page seems like signing people up for something they didn’t sign up for themselves- not where I would want to start in a potential client-coach relationship.

Thank you for your input.