Windows XP SP2 is compatible with DirectX 9.0c. If you got the WinXP with SP2 CD, then DX9.0c should already be installed along with it. Just like what threatlockz said, check your dxdiag and verify your DirectX version. If you do not have the 9.0c version, the NBA Live 06 CD has one.
As for Windows XP "multimedia" edition (known as Media Center Edition), it is supposed to be an OS for "media center PC's". A media center PC is an HDTV, mp3 player, Internet PC, gaming PC, radio, movie player all rolled into one.
Check to see if you're PC is a media center PC.
Based on the specs you provided, you are good to go with WinXP SP2. I'm also using a 256mb PC with GeForce FX5200 128MB (Radeon 9550 128MB soon). The SP2 installation significantly slowed down my PC, but with a few tweaks and optimizations I might say I am satisfied with the performance of my PC as of the moment. If security is not a main concern or if the function of your PC is just for home use, then SP1, a free firewall and antivirus program are already enough (as long as the antivirus and the firewall programs are updated constantly).