I don’t think admin approval or one week wait times for new users are good ideas, it would probably discourage legitimate new registrations.
Anyway, the approval thing is ridiculously common on forums these days. I don’t think it would be an issue, as long as there were mods actively responding to the requests.
Again, I think the wait time (whether it’s a week or a few days) is a good idea for new users in general. Send them an automated PM that says that they’re welcome here and we encourage them to read our rules and project pages and whatever. Maybe let them post in some sections but not all? They should definitely not be able to create threads or make 25 posts in their first hour.