No, you don't need to install SP1 and SP2 first. Just burn the downloaded ISO image to a disc. From the download link you provided:
Windows XP Service Pack 3 (SP3) includes all previously released updates for the operating system.
Just a suggestion. Since you're using Ultimate, why not install XP Mode? It runs inside Windows 7 as a virtual machine. If you uninstall Windows 7 and replace it with XP, you may have problems finding the correct drivers
drivers, etc. Not to mention long-term support which ends April 2014. Windows XP Mode - Install and Setup