$1000 will buy you a nice 20" LCD monitor these days, although I'm not sure how ideal LCDs are for DVD viewing. If you go the more traditional (and cheaper) CRT route, I'd look for one based on Sony's Trinitron tube.
I'd get a flatscreen CRT monitor. I've heard that LCDs aren't ideal for DVD viewing (ghosting, imperfect black level) plus their cost premium is a LITTLE much.
If you can fit one on your desk, a flatscreen 21" monitor should do just fine.
Viewsonic 19". But if your on a budget go to BESTBUY and get the 19" $149 Magview excellent monitor for the money. I have two and will buy more as needed.