The box says that you only need a 800 MHz processor and 256 MB of memory
How well the game works on a 800 MHz processor and 256 MB of RAM, I don't know. I would guess not well.
You also, more importantly, need a 32 MB GeForce 2 or better or Radeon 7200 or better. A GeForce 2 MX would work, a regular Radeon or TNT2 will not. I can't recall any of these cards ever coming with less then 32 MB of memory, although some integrated systems might be set to use less then 32 MB of memory of video.
A complete list of compatible 3D chipsets can be found here: http://eagames.custhelp.com/cgi-bin/eagames.cfg/php/enduser/std_adp.php?p_faqid=15596
Note that if you have Intel Extreme Graphics or a Radeon VE that a 2 GHz processor is necessary, but only if, and in those cases I would highly recommend upgrading your 3D card. A Radeon 9600 Pro ($100-150) would be your best best in the mid range. I have a GeForce 6800 GT that runs the game beautifully, but expect to pay $350-400 for it.
Also I would highly recommend upgrading your system memory if you have only 256 MB.