Welcome to the site! don't worry about the non private part. For the most part only you and your partner will be reading your writing, and maybe an occasional person who is checking out your writing if they want to partner. We are a super gentle community and I have never seen anyone shaming someone for their writing or anything like that.
if you havn't already, take a peek at
THE RULES and the
HANDY SANCTUM GUIDE. After that you can peek at the request threads to start looking for a partner and story idea that catches your fancy or make one of your own to get the people coming to you.
If you come across any questions as you explore the site, there are always some friendly faces in chat that can help!