Sounds like you need a decent all rounder. Unless you plan to use the machine for games I would advise against a seperate graphics card as they can often be noisy and require more power than the built in graphics chip on the motherboard, a decent board will allow you to do most taks such as online HD video or basic photo editing etc.
Most modern motherboards and chips are very energy efficient, If all you want is a decent machine that will do most things (with the exception of high end gaming) then something like this bundle would be fine:
Asus Intel P5G41TM LX Motherboard Free Delivery : Motherboards For Intel : Maplin
This is a standard socket 775 Intel processor and will take most modern Intel chips (not the i3, i5 or i7 stuff tho)
Add a all rounder dual core CPU like this:
Intel Celeron Retail Box Processor E3400 Free Delivery : Intel Processors : Maplin
which is relatively low power and very quiet.
Add a 2GB stick of DDR3 RAM:
Desktop 2GB DDR31333MHz DIMM : Desktop DDR3 Memory : Maplin
All in will cost just over £100 for the above parts. You will need to get a ATX case but these can be picked up anywhere and prices range from about £25 for a basic box up to a few hundred ££
Add the cost of a DVD/CD drive at about £15 and a 320gb Hard Drive for about £30
Total cost of build around £180 and this would give you a decent all round system.
You will also have to cost in the price of a operating system such as Windows 7 etc.
Just bear in mind for a 32bit operating system the max memory is 3.2GB any more will be wasted, You could put 2 of those 2GB sticks in and install a 64 bit OS and you can utilise 4 GB of ram. More than enough for most people.