If that's your computer then it's got a 300w power supply. You are probably good to about 150w of a GPU. http://www.tomshardware.com/reviews/gaming-graphics-car...
you'll need to look at the specific model to see what the dimensions are to make sure it physically fits in your computer.
the 560 i rated at 160w. This could be pushing it, since the watts of your power supply are shared across different voltages. You won't have for example 300w available to the 12v. I think you would probably be safer with something like a Radeon HD 6850 or HD 7850. If you want Nvidia, then a GTX 660 (not the 660TI) is probably the best choice. all of these are rated arount 130w. So just 1 extra pcie power connector.
If you have a standard ATX power supply in there it's probably a simple replacement if you want more watts.
Many thanks for the detailed and helpful reply! If I went for one of the cards you recommended, would I get a good performance and decent graphics out of Guild Wars 2? I can currently run it fine with no noticeable frame rate drop as long as the settings are all on fairly low - crank it up to best and I get a frame rate drop.
I want to upgrade to experience the game in all its glory, but I'm worried that if I pay for only a small upgrade, it won't be more than six months before I have to upgrade again (and buy another ATX power supply, it looks like) to play something else. Is it just a case of 'That's life'?