IMAP/POP is simple to install and set up and you should have everything you need already installed. Just configure your client to use IMAP and point to your server (I use Evolution but most clients support IMAP). In Evolution you just create folders with whatever names you want (works just like Exchange regarding mail folders if you are familiar with that). The folders actually get created on the server as separate mbox files under your $HOME/mail directory. It's great because no matter where you are and what client you have installed you have access to all your mail and mail folders on your server. Nothing is stored locally (well, some apps like Evolution will cache your mail locally).
Now, regarding server side filtering that is something I haven't really done although I have parsed mbox files for other projects. It appears there is a plugin for Dovecot for this called sieve:
http://wiki.dovecot.org/LDA/Sieve
There are also simple Perl modules for parsing mbox files you could write something that runs from cron (or however/whenever you want to run it) to read /var/spool/mail/$USER and parse it into the appropriate mbox files in $HOME/mail:
http://perl.overmeer.net/mailbox/
P.S. I also have Squirrelmail installed and you can access your folders in it just as well. I also used Horde/IMP for the longest time as a webmail app which is probably a lot more robust than Squirrelmail but a little harder to set up and configure.