Hmmm, afraid its a bit of a how long is a bit of string question in the computer world.
Basic rules are spend as much as you can afford on memory and hard drive space.
Stay away from unknown makes ( including the dixons/currys/pc worrd own brands ) cause they are a nightmare to get drivers for later. Try to stick to the big names as support for drivers / future updates etc will be better.
Try to go for th i3/i5/i7 or AMD proc, not celeron or deff no P anything (old )
As you say you only want it for music/internet have you thought about a laptop instead ? You can get a good cheap one for about £350 that will have 4gb mem with an i3 processor. You can always connect your old monitor /kybd/mouse to it as well.
I could throw examples at you all day but if you PM me how much you have to spend then I could recomend somthing for that price.
This Dell outlet is a good source and they all have warrenty: http://www.dell.co.uk/outlet