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Minimum Requirements
Windows 98/ ME / 2000 / XP
Pentium III 450 MHz 128 Mb RAM
600 MB Free Hard Drive Space
4 Mb Video Card DirectX Compatible
DirectX compatible Sound Card
DirectX 9.0 or higher (included on the CD)
 
Always the best upgrade if on a budget, you should be fine if running 98 or ME, if you are running XP then 512 is really what you want as a minimum.
 
well..

I got CK this christmas, and it's running fine without any problem.
Ck is actually the first Paradox game I haven't had any trouble with. About my computer, I will upgrade it with more RAM, but since I'm a Student I have a limited budget. (I have a laptop, so RAM is extra expensive)
 
Congrats, good luck!