First, no matter what you do, you should run the SharePoint Prescan tool, to determine any possible issues you may have with upgrading. Here is a guide to running the prescan tool.
There are many different migration tools and methods to migrate from SharePoint v2 to SharePoint v3. Microsoft has a TechNet article about the different (Microsoft supported) methods available, pros and cons, and how to perform each: Determine upgrade approach [Windows SharePoint Services]. There is a SPS to MOSS version available as well.
Generally the database migration upgrade method is the easiest (assuming you are not using a lot of customizations). This involves migrating the SQL database (if necessary) and attaching it to your new SharePoint instance (either through Central Administator or with stsadm -o addcontentdb). SharePoint will upgrade the database automatically.
In place upgrade will probably not suit you, considering you are not upgrading the WSS instance, but moving the content to a new farm.
A commercial tool that I have used is metalogix SharePoint Site Migration Manager and it usually does the trick. It uses the v2 and v3 APIs to copy content from your old instance to your new instance.