It looks like you want to build a really high quality but small entertainment center.
None of the 19 inch monitors fit the 1080i high definition standard. Viewsonic has a 1680x1024 which comes close. Samsung and a few others offer a 1440x900 which comes closest to the "letterbox" shape (width to height ratio) that movies are filmed in. That
screen resolution is closer to 720i than 1080i. With those resolutions and ratios on a 19 inch
screen, its going to look pretty good anyways even if it is not the best picture possible.
I would consider going up to a 21 inch or a 24 inch
monitor if it will fit. With those sizes you will be able to get a 1920x1080 screen making it true 1080i high definition. You could get 1080p if you buy a Bluray optical drive for your computer. This saves the space and
power requirements of a stand alone Bluray player. Be sure your
monitor has an HDMI port. It really would not take much more
money or space to get the best picture possible.