Well can't speak for UBB Classic as I upgraded from 6.5.1 Threads to 7.02
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I also have a dedicated Server 2003 w/1GB RAM and P4 3.0Ghz
My upgrade took just under an hour.
A few hiccups along the way mainly due to my non-familiarity with the software and processes.
As always, make sure you have a valid backup of MySQL, PHP, Website, and UBB before attempting the upgrade.
Then take another backup once you've completed the upgrade and before you start to customize it too much.