Gmail and/or SylpheedSylpheed
If your email server supports automatic forwarding or POP3 then you can configure it to forward your emails to a Gmail account. The advantage being that you can set up online filters asas opposed to the local ones in Thunderbird. That way, the messages will be filtered before downloaddownloading it so you don't have to keep the client program open.
Sylpheed is a lightweight email client that doesn't download attachments unless you click them. This results in an average email being 1 or 2kb in size. So downloading thousands of emails isn't an issue. It will just download the text part, and show the rest as additional attachments. It also has a portable version that can be installed on a USB drive and used on multiple computers.
Since the filters are now online, you can have an assistant set them up and the folders will automatically be downloaded to every computer that has the client installed.