The shelter in my area is amazing. I recommend trying to get in touch with them to see how they operate. I believe they have a grant from the state, and also rely heavily on donations.
Here's their website:. http://www.bunssb.org/about-buns/
I imagine if you email them the coordinators would be open to discussing the shelter logistics over the phone with you.
Each rabbit has it's own hutch/cage, and they have probably about 20 exercise runs. Each bun gets a few hours of exercise in larger runs each day. They rotate so half the bunnies get put out in the morning and half in the afternoon. Volunteers feed the bunnies, clean hutches, etc. The only time the bunnies are in the same run is if they are a bonded pair, then they are always together.
They also rely on fosters for any overflow bunnies, or bunnies needing medical care.
Unspayed/neutered buns are kept separate, and are spayed/neutered as soon as possible. The shelter works closely with a specific vet office, I'm not sure of the financial arrangement that they have worked out.
There's lots to think about, I imagine you would want to have a partner in doing this! But very admirable!
I imagine the no-kill cat and dog shelters could also advise you on how they function financially, because I bet it would be similar.