Use XP Pro SP3. Your machine is too slow(I assume the 1.25g is referring to RAM, not hard-drive) to handle Vista, and XP-home is not supported by Graphisoft. Also, ArchiCAD 12 isn't going to run very well on your hardware anyway. that machine must be at least 4 years old right?
Of course, you can't buy XP anymore though. What OS do you have at the moment?
Josh Osborne - Central Innovation
HP Zbook Studio G4 - Windows 10 Pro, Intel i7 7820HQ, 32Gb RAM, Quadro M1200
I have a 4yr old Pentium4 3GHz laptop with 2GB of RAM and it runs Vista VERY well!
However, there is no benefit to using Vista unless you are using Vista 64-bit Edition. For your hardware setup, you should use XP Pro.
The most important hardware components for smooth Archicad operation are (in no particular order):
Processor speed: you have a very fast processor already, just not as fast as the newer hardware available. Multi-core processors or hyper-threading helps dramatically with AC12, but you will need to rebuild the whole platform to use the newer hardware available.
RAM: 2GB of memory should be your minimum target. Having 3GB would allow AC12 to use the most possible while also leaving enought for Windows and other programs to run.
Video card: there are many, many, MANY good graphics cards available, however I'm guessing that your computer still has AGP instead of the newer PCI-Express slot. Your options are limited in this regard.