this slide deck has some good information around options for upgrading from SharePoint 2003 (SharePoint Portal Server) to SharePoint 2007 (MOSS):
This article has a lot of detailed information for this upgrade too:
Make sure SharePoint 2003 is patched to the correct level, and make sure SP2007 is at least SP2 for the upgrade to SharePoint 2010.
The fact there are no customisations means your upgrade path is likely to be smoother.
From the brief detail you have, the best option may be to detach the content DB from the SP2003 farm (after a pre-scan), and attach it to the SP2007 farm (which will cause a content DB upgrade). Then you can use the site from your SP2003 farm.
Of course there are other options based on your requirements and environment.
To upgrade to SP2010, make sure SP2007 is patched to at least SP2. You have different options for this upgrade too. Any customisations from your 2007 farm will need to be recompiled to be used in the 2010 farm.