I've been on the verge of starting a local community. I'll do it one day soon.
When I do, I would start with a website/blog, probably using Ghost. Good community starts with good communication. Comments are just fine for initial community building. Once you have some traction, consider a forum.
Also, look into Front Porch Forum, they've been doing it their own way for years, it can work.
However, my unschooled child loves maths and has...and much more...he's now doing maths at uni. He's also so deep into the philosophy world that my mind hurts just reading the titles of the books he buys.
I wish I had the encouragement and freedom to explore without judgement when I was that age.
Depending on the school, the smaller settings, the different and wider range of activities and support available. I'm particularly attracted to the Montessori way.
I'm concerned about schooled kids not socializing outside of their direct age group :) There's been plenty written about how unhealthy and damaging it can be to only be in a peer group of people your own age.
Honestly, the socialization is a myth. Homeschoolers socialize with all ages, that's healthy and educational from a huge amount of perspectives. e.g: kids can be become leaders by supporting younger or less able kids.
This topic has come up repeatedly in my circles in the past few months. When I asked people, they noticed at least these benefits of each:
1. Mixed-age groups let you hear perspectives across age groups. You might also have one group helping another in their weak areas. That didn't happen as much in same-age groups I saw.
2. Same-age groups give you people who can relate to you and your life. That might not exist at all in mixed-age groups depending on the age distribution. Some people in mixed-age groups told me they switched to same-age groups for that reason.
I'd be interested in looking at any studies on this topic. Since you mentioned "plenty written," do you have any links we can look at?