Martin,
First, make sure that you have enough 2003 TS CAL's and a licensing server as those are going to be required as the licensing for TS 2003 is more stringent and not as lax as 2000.
Now as far as upgrading goes, if all of the installed applications on the existing server are win2k3 compliant, then an in place upgrade will work just fine. I have personally just completed 2 such upgrades within my domain.
Essentially put the install CD for Win2k3 in the server and follow the prompts.
