I think the OP is about having a card with at least the power to run the screen at native rez. What else is in the system.
As for screen resolution, yeah, most cards will have no issues with 1920 x 1200(16:10) or 1920 x 1080(16:9). I guess if you have a non wide screen you would run 1920 x 1600(4:3). Either way, I had a Geforce 4MX(old media center) running 1920 x 1200 without issues, so any modern card will be fine.
You can run a LCD under its native resolution, but it tends to make things a bit blurry(the amount of blur depends on the screen it self, some are better then others).
Now on to picking a screen
LCD's have 3 general panel types.
TN - Cheap,low viewing angles(dont look at the screen from far above or below),fast response,ok color
PVA-More expensive, way better viewing angles, good color(even from most off center angles), not as fast as TN
IPS-Expensive,best viewing angles,best color,slowest response times,good for photoshop users.
For most gamers TN is the way to go as its fast. I personally have a PVA, but for some users its a bad idea. I just cant stand bad colors and low viewing angles.
I personally recommend you look at a local store for displays as everyone has different expectations. Samsung has some fairly nice screens out(but also some cheaper ones).