I haven't yet read any other reply, so I don't know if anyone else has touched upon any general ideas about the OP's question. There are two different ideas I would offer, one to suggest a monitor that meets his $1,000.00 limit, and another which discusses the framework for a truly workable PP set-up.
First of all, the way things stand now, you want a monitor which uses an IPS panel. Sometimes it is difficult to find out what type of panel any given monitor uses, as manufacturers don't always disclose this. The differentiating characteristic of the IPS panels is an evenness of illumination when your viewing angle changes from straight center to off-center, either vertically or horizontally, plus IPS panels are capable of displaying a greater color space than most other panel construction types as well. Second, you want a monitor that has been well made with a non-defective panel and superior electronics and adjustability. Third, a monitor for this kind of work should be 24" or larger, if you want to work at convenient image sizes. Last, the best monitors for PP also are capable of displaying a color space near or equal to 100% of either Adobe RGB or at least the sRGB space. Eizo, NEC, Dell, HP, and perhaps some others make several monitors which fit this description, and some of them are under $1,000.00. Look up reviews and tech specs to judge what looks best for yourself.
Keep in mind that what you do with your pictures may be decisive in picking a monitor. For instance, if you will never routinely have any of your pictures published on an offset or other kind of commercial printing press that requires a display color outside of sRGB - like some of the subtractive CMYK-type colors that fall outside it - you will not need a monitor which displays a color space "bigger" than 95% or 100% of sRGB, and these monitors will usually be less expensive than the ones which cover the Adobe RGB space. Last, as with many otherwise good IPS panels sold today, one must be careful to avoid accepting one with color that displays "unevenly" across the screen (if you display a full-screen neutral gray rectangle in Photoshop, does it look like the same color from left-to-right?). Just a small unevenness is inevitable, a really noticeable difference is unacceptable. This is a common manufacturing defect because of how the panels are constructed. Last, you should also purchase a monitor calibration package, consisting of a colorimeter or spectraphotometer and matching software from X-rite or other reputable companies. This is a necessity to get your monitor to display properly so that what you see is actually what your file should really look like.
As for what I use, it is an NEC 30" 3090, complete with the NEC-customized colorimeter and matching Spectravision II software that goes with it. This combination is extremely good, plus it allows me to instantly switch between stored and very accurate monitor profiles like sRGB and Adobe RGB that the software, especially tuned to the monitor, can pretty easily produce. The color consistency is very good across the screen (a first one, returned to the seller, wasn't as good in this regard), evenness of illumination is very good, color accuracy, sharpness, geometry, contrast and brightness range are all excellent.
First of all, I'm now a PC guy who used to be a Mac guy, but Macs are great too, so my example here can be replicated or bettered on either a new PC or a Mac, depending on your own preferences; either one can be a great machine for PP. My computer is an exceptionally good custom made PC (made by highly regarded builder Puget Custom Computers a few years ago). It runs Windows 7 64-bit Ultimate and tons of graphics software. It's got an i7 960 3.2 GHz processor, an Nvidia GTX570 video card (newly added), 24 GB main memory, 4 drives (2 160GB solid state drives plus 2 fast 2TB 7200 rpm disk drives), USB 2 and 3 ports, a Blu-Ray burner, lots of very silent high capacity cooling, and a few other things as well, like an external attached 5-bay 10 TB Drobo for backup. You don't necessarily need something this complex and expensive. However, just remember that if you try to buy one that is just barely adequate, it will be out-dated and ill suited to the future that much faster than a better specified one. Buy the best you can afford, so that you can run it longer without being crippled in your workflow.
The best rule of thumb for most computer components is this: figure out what types of components (by general performance and function characteristics) that you need and, whenever possible - except where it might affect reliability and longevity - buy the second best or fastest, not the very best or fastest, performing component in that category; this method will give you the longest possible use of your computer at a fairly reasonable price.