Monitors seem to come in 1080p resolution as the standard (same as HDTVs). Now how much that monitor costs completely depends on other quality factors, but your graphics card won't care about that. Targeting good frame rates at 1080p is a generally good target for new gaming systems.
As I mentioned, the price on such a monitor depends on other factors. The System Guide I linked discusses this on the last page, but the primary factor is the technology used for the LCD panel. You can get something like this
for $150, which (I'm assuming) uses a TN panel. The drawbacks to this technology are poorer color definition and limited viewing angles. Personally, I think this is passable for most situations, but it also means always looking straight at the monitor and obviously not having the best color quality.
If you are willing to pay more for a monitor, however, IPS displays have excellent color definition, and I've noticed that all displays with resolutions higher than 1920x1080 seem to be IPS as well.
Save yourself the trouble and don't ask why the TV remote is in the refrigerator.