I would go 19". it's bigger! If you don't want to watch movies on your PC then I would just go normal.
Response time. If you are playing games then a lower response time is better otherwise the game graphics will tend to "bleed" when they're moving as the monitor can't keep up with the game.
DVI - All monitors will have the blue analogue connection, some will also have the DVI connection. If your graphics card doesn't have a DVI slot then there isn't a real need to get a monitor that has a DVI slot. However, more modern graphic cards only have DVI slots so you'd have to get a DVI slot monitor. To future-proof your monitor, I would get one with a DVI connection.
Active Matrix - I would. TFT monitors have it already.
Contrast Ratio - The higher the ratio the better.