Just starting to eval SharePoint for document sharing/storage.

My server is running and I've created a directory tree. I have a
few different folders under the default 'documents' location. Each
of these folders have only one coordinator.

The problem we have is that our test user group consists of mainly
users who also reside in the Domain Admins group. I have tested
with a general user as well.

The users in the domain admins can see every folder under the
default 'documents' and they can "Check In" to any directory they
want. They can't publish to that folder. My general test user
doesn't see the folder at all.

We need to be able to block all un-authorized users from checkin-in
documents to folders that they shouldn't have access to. (I know
that this is limited to our Domain Admins group right now, but our
Finance department is looking to utilize this and the don't want any
other eyes but their own looking at stuff).

Does this make sense or do I need to clarify further?