There are lots of ways to run a partnership. I would, like others, suggest not offering equity, however. Equity is one-time, and upkeep is forever--I don't think you'd get any serious takers. Better to sell half outright. Deals where one side puts up more money and the other puts up more work (or some other resource) can work well, though.
If you are selling part ownership, even (and especially) to the best of friends, put it in writing, and include provisions for one side not holding up their end of things and for how it works when somebody wants out. (I've been there and done that, and having expectations all clear and explicit on paper saved a lot of stress when one partner was laid off and couldn't hold up his end of things. Having it be cut-and-dried in writing is probably the reason we're still friends.)