What happens? Does everybody go to 0 reputation, and gain it up? Does the original proposer get reputation to start out with, or what?
Area 51 and the Stack Exchange sites have separate reputation systems.
Once a site is created, everyone starts out with a reputation score of '1'. You will earn an initial bonus of 100 reputation if you have at least 200 reputation on another site. But, essentially, everyone starts out on the new site with a new reputation score and work their way up from there. Your reputation from Area 51 has no connection to that process.
The reputation gained during the beta phase is kept.
The proposer gets reputation on the proposed site as any other users: from votes for the posts the user writes, and from proposing edits that are accepted. The proposer gets reputation on Area 51 for each user that commits to the proposed site.
The reputation on Area 51 and on the proposed site are not linked; when I log in on the site that reached the private beta phase, the reputation I have on Area 51 is not used to calculate my reputation on the new site, in the same way my reputation on a Stack Exchange site is not used to decide my initial reputation on another Stack Exchange site. The only exception is when I get the extra 100 points because I have reached a reputation of 200 in a Stack Exchange site.