Membership and sub sites access

Hello All,
I have a membership site and decided to build the forum as a separate sub site. The main site is run with the membership plug in. I would like the forum to be totally private to non logged in users.. Only members of the main site can find and access the forum. I do however want the members to be able to log in the main site and be able to access both sites without logging in a second time. .
Should I set up the sub site with a separate membership install?
Should the site be added as a url group in the first/main membership install? What is the best way to set this up and how do I do it?

BTW: I still have an opent thread on Events+ that is pretty urgent. I imagine when I hear from the client tomorrow morning he will want to move on if not resolved. I hope to prevent that.

Thanks for all you help.