What should I be looking for in a low cost color correcting monitor?
There's a loose binning of monitors into 3 categories:


Consumer equipment [$500 - $1500] Dell U-Series LCDs, Panasonic Viera Plasmas
Entry-Level Monitors [$2500+] FSI, HP DreamColor
High End Monitors [$$ - $$$$] eCinema, TV Logic


Some of the features of non-consumer monitors that you'll want to learn about are:


HD/SDI inputs
Additional outputs
Colorspace and signal type support, such as 4:2:2
"Higher" bit depth, such as 10-bit
LUT programmability


If you're asking for low-cost, without already knowing these monitors, then I strongly suggest you stick to the first category, and use something like the DataColor Spyder calibration puck.  Getting that top 5% of color accuracy comes at a steep price, and since it seems you're just starting out, you probably want to stick with the 95% solution.  Upgrade only when you have specific need for the features.