Q: Will it put too much of a strain on the processor? For example, I just got a flat-screen monitor with a maximum resolution of 1400x900. This is quite a bit higher than my previous monitor (1024x768).
A: as zbalat already mentioned lcd's have a native resolution which normally is the same as their max resolution. This is the resolution you should use. If you use any other the image will not be as sharp since it will have to be rescaled. Playing games on higher resolutions may cause your game to slow down (lower framerates). This depends on your graphics card and processor. You could have to lower your resolution to play some of the newer games.