It really depends. If you're bying monitor and keyboard/mouse I think it's more important (or at least equal) to get these things right. This is because they often stay with you for more than one computer generation (at least if you upgrade a little now and then and don't sit on the same computer for 5 years). So the next time you can skip these and put more money into the goodies.
When you say purchase a computer, do you mean like 'purchasing' the whole thing as a set, or build your own?
It would make a difference because you can really choose the mobo when purchasing the machine as a package - therefore it would be important to find a reliable computer with the best specs so that you won't be needing to upgrade for a while.
On the other hand, if you're building a computer from scratch, I think it'll be important to find a reliable mobo that's long lasting, while choosing a CPU that gives you the biggest bang for your buck (doesn't matter if it's not the fastest CPU on the market since they're not usually worth the money.)
In addition to this, it's also important to plan in advance what you want to store on the machine. Hence you'll need to choose a Hard Disk that'll be suitable for your needs.
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.