My general rule of thumb is to use high-quality displays with IPS or IPS-based LCD technologies. Unless youre doing pro-level print work, you dont necessarily need a professional-grade monitor, but you do want a display that will fully support true 8-bits-per-pixel color. IPS displays used to be fairly pricey, but their cost has come down considerably. You can find good-quality 24-inch IPS monitors supporting 1920-by-1200-pixel resolution for under $400.
Similarly, if youre looking at laptops, try to find one with an IPS panel. They exist, but they tend to be among the more premium models. Asus, Dell, HP, and Sony all ship laptops with IPS displays. More pixels are better on a laptop, as well--look for a native resolution of 1600 by 900 pixels or better.
Note that many modern LCD screens offer wide-gamut options. Be sure to set Windows to display the correct gamut for your monitor. Just type color management into the Windows Start menu search box, select Advanced Color Management, and then choose the Advanced tab.
Youll also want to set the correct ICC profile for your display. Usually you can find the profile included on a CD that ships with the display, or you can download it from the manufacturers website. If the process seems a little overwhelming, you can bypass all these confusing settings by using simple tools to calibrate your display.
Monitors: More Is Better
More pixels are better--and more displays are also better.
On my desktop system, I have three 30-inch displays that each support 2560-by-1600-pixel resolution. My main display is an HP ZR30w, which is technically capable of 10-bits-per-pixel color. I also use an older HP 3065 and a Dell 3008WFP, though the Dell often pulls double duty by being connected to one of my test systems. I've calibrated all three using the Spyder 4 Pro calibration puck and software.
You dont need three displays, but having two is extremely handy. Generally I run Photoshop on the ZR30w and have Adobe Bridge running on the 3065. Even lower-cost applications, such as Lightroom, support dual displays. Simply put, having two monitors makes your workflow more efficient. Note that you dont have to use two high-end displays--the secondary monitor can be a lower-cost model, though having similar displays is ideal for calibration purposes.
Photo editors, like cameras, are merely tools to get the photograph. The art and craft of the photographer are what really makes photographs shine. You get better as a photographer only by shooting and editing photos. Having the right PC hardware and software, however, will make editing chores just a little bit easier.