To keep other threads clear of the inevitable "Will my system run this game" posts, please ask the question here. Myself, and other knowledgable members of the Halo 2 Vista forum, will asist you and give advice.
While the game will run on Windows XP with the v0.3 H2XP hack, it is notable that the game will have sporadic performance in menus, multiplayer known to be inaccessable, there is a problem with continuing past the Gravemind level, although there are workarounds, and all in-game videos (not cutscenes) do not show. Also, the Halo 2 Map Editor cannot be installed on XP. That's quite a number of reasons not to bother.
Ideally, you need a version of Windows Vista to run this game the way it was meant to be played. All versions of Vista support the game, including the 64bit and Business editions.
A reminder that the Minimum System Requirements are:
CPU: 2Ghz Single Core, 1.5Ghz Dual Core, Any Multi Core
RAM: 1Gb
Video Card: 128Mb and fully supports Shader Model 2.0 and has a WDDM Vista Driver installed (Geforce 6100+* or Radeon X700+**)
Hard Drive: 7GB minimum, including extra for swap file if you have less than 1.5Gb of RAM memory.
The Recommended System Requirements are:
CPU: Dual Core, 2Ghz or faster clock speeds.
RAM: 1.5Gb
Video Card: 256Mb with strong SM2.0 support (Geforce 7600GT+ or Radeon X1600+)
Hard Drive: 15Gb (extra for Map Editor and Dedicated Server)
*Geforce 5 FX series of cards simply too slow in SM2.0 to run the game acceptably.
**You can get away with running the game on lower cards in this Radeon range, however their bad performance in SM2.0 will cause low in-game framerates.
P.S. The game may run on integrated graphics solutions, but only if they support SM2.0 and have WDDM drivers i believe. Ask and i'll assess the chipset model in your system.