OK first thing.......DONT buy and AMD chip.....
That is an awesome budget and considering you have a monitor even better.
I would suggest the 6 core extreme CPU as it can be overclocked very well. I would suggest sandybridge but I have recently learned they are having problems with a faulty interface which may affect a hard drive dropping off and disappearing.
MOBO wise stick with ASUS or EVGA.
6GB of 1600mhz ram will be plenty for a gaming rig - three 2GB sticks.
PSU - go with an enermax 1200watt supply. People may argue that this is massive overkill but it gives you incredible stability and loads of PCI-express power supplies, if you want to run an SLI set-up on your graphics card.
Graphics - NVIDIA 580 all the way and if you can buy two and stick with EVGA, they offer a 10 year guarantee if you don't over clock them, and you wont need to.
Get an SSD - Crucial C300 256GB as this is a faster drive than the 128GB.
Win 7 Pro not ultimate! Pro is perfect as it has backup software.
Case - If there is money left go with LanLi for air cooling, or silverstone if you want a water cooling rig.
The only pitfall is your monitor wont support any higher resolution. If you can i would suggest eBAY for a DELL 24inch monitor 1900 x 1200 res or higher.
I have had a quick look on-line and what I have suggested is coming out just over £ 2500 but if you remove one of the 580's you will be under budget.
I wish I had you money as this would be a fun day building this rig!!