I've had a bunch of different formats.
My first experience was when I became a peer support worker at the recovery house I attended after I left. I did that for about a year and a half and I loved it. I worked several shifts a week. Mostly I was there to just make sure nothing major happened and to talk to the other women. To share my experience, strength and hope. Hearing their stories was empowering and encouraging for me, and being able to share for them that they were not alone was cathartic for all of us.
I have been in group settings that were not leader-based. That was awesome too. We did exchange phone numbers, and when that particular program lost funding and had to close down we all stayed in touch. It's been about three years and we have been getting together once or twice a year as a group still, and catching up.
I also have a big peer support network, as all of my friends deal with a history of addiction, mental health issues, abuse, or a combination of the above. We help each other get through the worst of it and do positive, fun things together. That has been more of a support to me than any meeting or recovery program or therapy group I've ever been a part of.
And lastly, I am in a mentoring program for people with eating disorders who are recovering. My mentor is amazing. She's younger than me and she is constantly encouraging me and sharing her own experiences and struggles and victories. I can be completely open and honest with her.
And then let's not forget about PC, which in itself is a huge peer support network.
It sounds like you have a cool opportunity with those people. I advise checking it out. It couldn't hurt. Some great things start that way. Good luck.