T
Murphys Law states that as soon as I've spent the money
upgrading the old one, it'll vanish in a puff of smoke. 
I think you'll find that's Moore's Law

Anyway starting with hardware...
RAM: 1GB min, 2GB preffered
CPU: Dual-core, 1.8ghz
Hard disk: 80GB min
Graphics: Integrated, shared video memory
Optical drive: for the price, may as well get a DVD-RW
Thats about the basics you'll need for a modern computer. The more RAM you have, the more stuff you can have open at once without fear of the dreaded Windows slowdown.
As has already been said, avoid Vista. Whatever anyone says, it's still crap. I went to MS SQL 2008 launch party and we were told in a seminar (by Microsoft!) that Vista was basically built on top of XP. Only it has a load of crap added nobody wants, which uses up valuable resources and makes the end-user experience god-awful. Vista is not the "fresh" and "new" operating system everyone thinks it is. Stick with XP but make sure you get service pack 3 and a good virus scanner.
Good free virus scanners include AVG and Avast!. Always better to get one with some level of support though, but avoid anything made by Symantec, Norton or McAfee - resource hogs. I recommend Kaspersky Anti Virus personally.
Ebuyer.com have some really good deals on all the time - I'd recommend them all day long. Dell are also quite good. I'd just phone them up to get the better deals, as they can go a lot cheaper than their website advertises. I managed to get a £750 laptop down to £499 (I was buying 22 of them though!).
Wouldn't set foot in PC World if I were you. You
will get stung somehow.