The size of the monitor is totally irelevant and virtually any video card can drive any monitor with a suitable connector. (That's what we have standards for.)
Now, gaming performance depends on the screen resolution - the amount of pixels your video card has to draw. Whether your new monitor will make things go slower depends on what resolution you use at the moment and what you decide to run your game at in the future.
LCDs look good only at their native reolution, so unless you want the game look ugly, you'd have to run it at 1680x1050. This means 1.8 million pixels to draw. Compare this to whatever your current monitor is set to.