I would say Processor is important, RAM, you can get away with having about 256mb on WinXP, but 512mb reccommended.
As suggested before, if you like gaming, you would want a decent (at least 128mb) grapihcs card and also, a good soundcard that supports EAX. If you like listening to music, then you can get away with a shoddy built-in soundcard, like my old SigmaTel chip on my motherboard. The music quality was good, but games where all crackly, so I upgraded to a Philips 4.1 soundcard.
You will also want a good size HDD, say 80gb+ from a good manufacturer like Western Digital, Maxtor and Seagate (im not sure if there are any other HDD manufacturers as it goes
).
You can't really say which is most important because in the end, you need all of that stuff for the computer to work, it's just a case of the more money you spend, the better/faster/more reliable the product will be (thats how it should be anyway). Stick to known brands and check for user-reviews on websites etc. so you know how good a product is from people who have tried and tested the product.