Mozilla will take over my database of emails (in the thousands) and my inbox directory tree?

I moved from OE to Mozilla about six months back and think it's very good. All my messages were imported completely fine, although your email accounts will be listed with their own separate Inboxes etc. and there is a "Local Folders" list which is like the standard OE setup. You need to add a rule to each account to move the messages into the Inbox of the local folder.

Gareth