At that resolution I recommend you spend slightly more for an HD5770. It is really the minimum current generation card you want for that resolution. http://www.overclockers.co.uk/showproduct.php?prodid=GX...
If you really can't spend more then try to find an HD4870 somewhere for that price, perhaps used.
There are no 256-bit HD5770s. It does have DDR5 memory however which makes up for the narrow bus in terms of overall memory bandwidth.
You will find some 512mb HD5770s however. I would avoid them at a high resolution like yours.
HD4870s are all 256-bit. Once again a 1gb card would be preferable.
In general the HD5770 and HD4870 are about equal in performance. The advantage of the HD5770 is DX11 compatibility and much greater power efficiency.
I would get the HD5770 over the HD4890 myself, even for the same price.
Also the resolution you originally listed is much higher that your actual resolution(by about 50%.) A lower resolution means less graphical power is required. The HD5770 will be very good for that resolution and if you would prefer to stick to your original budget even an HD5750 would do quite well; http://www.ebuyer.com/product/179465
Or for something even much cheaper the HD4850 isn't that far off the HD5750(although it isn't DX11 and uses much more power); http://www.overclockers.co.uk/showproduct.php?prodid=GX...
Keep in mind your motherboard is crossfire capable and your PSU can actually handle 2 of any of the cards I just recommended. As an example two HD5770s in crossfire are on par with an HD5870. I wouldn't recommend adding a second though until you upgrade your monitor. If you like the idea as an upgrade path though I would recommend the low power/heat DX11 cards even more so as they will make for a more appealing dual card set up later on when DX11 is more widely used.