How will you legally upgrade without a copy of Office 2003? It is a new version and you need a new license. There are upgrade versions available. If you need Access and/or Publisher you will need one of those - if not see below. Frontpage and OneNote are standalone apps for most versions of 2003 (unlike O2002).
If you run the installer of a commercial copy of Office 2003 it will automatically upgrade earlier versions of Office and retain most of your customisations and any internal data (such as emails).
The cheapest way to upgrade is probably the "Student and Teacher Edition" which you can legally install on up to 3 computers. In theory you can only use it if you work in a school, are a student or a parent of a student but the pack is supplied in full via many normal retailers (such as Amazon) and doesn't require proof of status. It is effectively a Home version (but all the apps are complete) - but MS didn't want to call it that!
Actually it is a good time to grab Office 2003 as there are some good clearance bargains knocking about with the 2007 version due out anytime soon and also the student version of 2007 won't include Outlook which is a real shame and in my opinion will just push the home market even more towards open source solutions.