Hi cyfan.
Sorry to say, but you have not been given very relevant advice here.
Audio work is really rather simple for a modern computer and does not require very much resources when you compare to editing video or running some games. So basically any modern computer will do. Things has really changed over the last few years.
Audio programs generally do not rely on a lot of RAM memory. Instead they work directly towards the hard disks. The exception is samplers (a special kind of software instruments) that will run faster if there is available memory.
So what you want to look for is a decent computer with decent hardware. Nowadays that generally means a dual core CPU and 2 or 3 Gigs of memory. You will like decently fast harddiscs but 7200 rpm really is enough unless you go above, say, 30 channels.
Do check carefully if your software will run on the new operating system, far from guaranteed. Seems like it is getting more or less impossible to find XP systems nowadays, most are Vista. And it can be difficult to downgrade to XP while some programs simply does not run in that environment. Vista is fine though, works for just about anything if set up with some care. But again, not all programs runs under vista.
If you have a good sound card already you might want to take that to your next computer. Not all computers has the older type of bus where you can put the card ( called PCI, as opposed to the more modern PCI-express ). Not all of these cards has drivers available for Vista either.
Next thing is that you probably would want to be future proof. As always, more memory and faster processor is better. But the bleading edge stuff is always bleeding edge expensive as well. You have to make the balance there somehow. My experience though is that it often is non-economic to buy more than you need right now. In a few years time the difference in cost between "enough" and "future-proof" will buy you a completely new system with a lot more capacity.
As for 64 bit OS, there is not really that much to talk about. Currently very few applications can take advantage of it, very few hardware systems really support it, and you rarely do need it. This might of course change over time, but currently it is bleeding edge.
// Gunnar