This is one of those things, that if you get really 'into' it...you can sink a lot of money into it and drive yourself crazy trying to get it perfect.
I wouldn't really recommend a cheaper screen. Most of the cheap flat panel screens use a technology called TN (twisted nematic). They are inexpensive, bright and responsive...which makes they great for games, movies and general computing. But for photographic editing, they are lacking. For one thing, most (may all) of them, can't display all that many colors. Off the top of my head, it's something like 6 bit color, with a smaller gamut that sRGB. Yet a good photographic workflow edits in 16 bit with a much larger color space. So the monitor can't come close to displaying the colors that may actually be in the image.
Another issue, is that TN panels tend to have terrible viewing angle changes. If you move around, the display looks different to you eyes...so in order to keep your edits consistent, you'd have to be in exactly the same position every time (not likely).
So a better screen technology is IPS (In Plane Switching). These screens have a much better consistent viewing angle, and I think they are better in terms of the colors they can display etc. They are more expensive, but they used to be $800+....you can get them now for much less.
Of course, you can get professional image editing monitors that come packaged with a calibration device and can display colors almost up to AdobeRGB. Very expensive though.
But even if you can only afford a TN type monitor (or just keep the one you have), calibration is key.
The popular ones are the
Spyder from Datacolor.
The Color Munki from x-rite