Looking at various makes and models of TFT monitors I see various maximum resolutions given, such as 1440X900, 1680X1050, 1280X1024. Would there be any advantage in buying one with any particular setting. Thanks.
In very, very general terms, the more pixels you have in the display, the more detail it will have in the 'picture' and, therefore, the better it will look.
So again in general terms, and depending on your budget, it's best to go for a monitor with the highest 'native' resolution. For example, a TFT monitor advertised at 1280x1024 would have an X/Y matrix of 1.3 million pixels. Whereas a 1600x1200 monitor would have 1.9 million pixels. Both have an aspect ratio of 4:3 (just like a standard TV) but the higher-res monitor display will look simply oodles better.
Note that, as X7-250 says, the other two you mention are 'widescreen' versions; not quite the same aspect ratio as a 16:9 widescreen TV, but close. A widescreen monitor will look much better if, say, you watch video or DVD on it or, for example, wish to have two windows open on the same screen, side by side. Or a double-page spread.
So in general (but it does depend on your needs), we would tend to recommend a widescreen monitor, with the highest 'native' resolution you can afford. There are some extremely tasty 1680x1050 models available at quite reasonable prices. HTH.