First, r.e. VGA vs. DVI ==> at the resolutions you're considering, it will make no noticeable difference. DVI is "better" from a technical perspective, but you will not be able to tell the difference. So if there's a cost difference, save your $$ and go with a VGA input. [24" monitors with 1920 x 1080 resolution are about the smallest monitors where the DVI input has a noticeable quality improvement over VGA]
Second, r.e. the size of the display: A 22" display has 21% more area than a 20" display ... this absolutely makes a BIG difference in the readability of the display. If you don't want to (or can't) buy a 22" display, I'd go with a 19" with the 1440 x 900 resolution. This will have almost exactly the same pixel density as a 22" display [A 22" display is 34% larger than a 19" monitor and has 36% more pixels ... so the pixel density is almost exactly the same].
For watching movies, you'll not notice any difference (other than the screen size) between the two displays. For gaming, it depends on how the game scales to larger displays -- if it uses the additional pixels to show more details, then the larger display would be nicer; but if it simply scales the same landscape to the display, you'll likely not notice any difference. By the way, as I suspect you know, your 9800GTX has plenty of horsepower to run most games at either resolution.
Bottom line: I'd get the 1440 x 900 19" display unless you can spring for a 22" monitor. The interface (VGA vs DVI) doesn't matter.