Right first you'll need to buy the bits... http://www.scan.co.uk
is the best of the bunch I'd say in terms of customer service. When I set up the computer shop I used to be involved in these were the best guys by far for general items.
As the other guys have said; http://www.ebuyer.co.uk
have got excellent prices. I normally buy my monitors through Aria as they're dead cheap and prompt with their service. A friend of mine had a lot of trouble with ebuyer, but I've heard a lot of good things about them. http://www.dabs.co.uk
is okay too. Between them you should be able to get bargain parts. I wouldn't advise getting things from eBay just in case. Oh yeah, heard alot of good things about http://www.overclockers.co.uk
Building a computer generally is quite simple, a few warnings before you kick off though...
Static kills chips!
Heat kills chips!
People not thinking kill chips!
So when building you can earth yourself using an earthing strap around your wrist or contacting the computer case which is set to ground.
Also something worthwhile bearing in mind, when the computer is plugged in the mains it is technically "on". So if you start pulling memory out or CPUs out you might start killing stuff, so keep those computers unplugged when you're working on them kids.
On the subject of what to buy, get a real decent case, I don'tmean one of those £20 jobs with the see through (who wants to see the dirty bits of computers anyways?), get a really solid case that's not going to slice your fingers off inside.
Here are two examples of some nice cases... http://www.scan.co.uk/Products/ProductInfo.asp?WebProductID=137412
The last one is pretty cool featuring dust filters etc, we used to sell a shed load in the shop as well and never got any returns. (I would bin the PSU included with it off though).
Another very important thing to consider is your power supply, you can get PSUs for a tenner, but they will be VERY poor, it can cause system instability and possibly have very bad consequences, I've seen crappy PSUs go on fire before now. One brand that I tend to use a lot is HiperPower, good quality and on the cheaper end of things... http://www.scan.co.uk/Products/ProductInfo.asp?WebProductID=408083
This is one with a bit of beef, if I was doing a build for myself I would be tempted to get this one...
Again as mentioned before ASUS are a good brand of motherboard, had a bit of a dodgy spell with some of their Socket A motherboards, but now they're spot on. In the firm I'm working in we're phasing ASUS machines in, and not had a problem so far...
I would also go for the Athlon 64. A note on the CPU, when fitting it be VERY careful, because you don't want to spend HOURS bending all the tiny pins back if you bend them trying to get the CPU in the socket, it should just drop in. Also, most CPUs (unless they're "OEM", which means they come with no packing etc), will come with a CPU fan. Normally the AMD ones are "okay" and come with a square of paste on the bottom of them with a tab over it, you need to pull this tab. If I had a quid for the amount of fan/heat sink combos with the tab still on and the CPU dieing I'd well, I'd probably have a few hundred quid...Also make sure you don't put the CPU fan on backwards, this can break the CPU itself and/or make it overheat.
Ram-wise I would go for Corsair, lifetime guarantee!
Your soundcard will more than likely be included on the motherboard, as will your Ethernet network card.
Before turning on too, make sure *everything* is seated properly i.e...
PCI cards (the PCI spec' says they're hot swappable while the PC is on, but I wouldn't go there)
RAM (make sure the two while tabs on each side are in the grooves).
As for what you want you're best of finding the bits in your budget and doing a google for some reviews.
Another thing I would strongly consider is buying a genuine copy of Windows XP, a lot of people don't take this into account and think they can just razz a pirated copy on their computer, but it's getting a ball-ache now patching windows if you're a pirate. Have a butcher's how cheap it is... http://www.scan.co.uk/Products/Products.ASP?CatID=37&FilterCategories=92&Thumbnails=yes
Once everything is in the box alls you need to do is set up windows, you don't need a floppy drive for this as you can just boot from the CD, however some SATA hard disk systems require drivers for windows to find the controller, which, again on some systems come on a floppy disk, so it could be worth picking one up (considering they're about £4 these days).
Once windows is in, you need to install drivers for your hardware, and get some security software installed... http://free.grisoft.com
for your virus checker (AVG free edition) http://www.lavasoft.de
(Ad-aware SE, a not too bad spyware solution)
Windows comes with a built in firewall these days, it's not bad, not amazing but not bad, I would be tempted to buy a router (unless you already have one) with a built in firewall for a bit better protection...
Anyhoo, I think you should be okay...if you do get stuck you're always welcome to give us a message...
Just posting an edit. Sorry to disagree with you BeemerRacer28, but I've found that Maxtor drives aren’t really very reliable; they're only a few quid cheaper than others like Western Digital etc.