Juancitox

For your budget it is a bit difficult to find something that you need. It's definitely half the price of a professional grade monitor, so those are out, obviously.
We have to look at high-end consumer grade monitors. So you have to forget programmable Look Up Table, uniform back light, and not as great color accuracy, but still good. It will depend on how accurate wise you need the monitors to be.
 
My suggestions are:
 -> ASUS PA246Q. It is a 16:10, 1920x1200  monitor, of course. It features a High-grade CFL back light for way better whites than white-LED backlight. It uses a true 8-bit P-IPS panel, comes with 2 pre-color calibrated profile with report: sRGB and Adobe RGB profile (this is great if you don't have a color calibrator, while there is no denying it's a quick calibration and you can get better results with you own color calibrator, if you don't have one, it's better than nothing). Has VGA, DVI and DisplayPort as input. Has a 10-bit Look UP Table, and 10-bit color processor, if I am not mistaken. It supports 10-bit colors via AFRC (emulated, as it is a 8-bit panel). Fully adjustable stand, and nothing glossy (maybe the red stripe is glossy, I am not sure). 0 wobble
 
 -> Dell U2410. It is a 16:10, 1920x1200 monitor. It uses an H-IPS panel from LG, It is an old one. Its being sold until stock is empty, as the U2413 replaces it. Because of this, it makes the U2410 quiet a good price (U2413 is too expensive). The response time of the U2410 is excellent for an IPS panel, and really competes close to high-end 60Hz TN panels. It uses a 12-bit color processor, and 10-bit Look Up Table (The 2 extra bit for the color processor over the Look UP Table is useless sadly, as the Look UP Table is only 10-bit, but I guess they got it for performance reasons when processing less colors). The monitor uses high-grade CFL back light instead of white LED. And as inputs you have everything: DisplayPort, VGA, 2x DVI, HDMI, and Component and Composite. You can plug anything on it, pretty much. It also, comes with 2 color calibrated profiles with report, (again, quick calibration, it's consumer grade monitors): sRGB and AdobeRGB color profiles. It uses a true 8-bit panel, and able to produce 10-bit color via AFRC (emulated 10-bit). Fully adjustable stand, and nothing glossy. 0 wobble.
 
 -> Lastly, the ASUS PA248Q. It is a 16:10, 1920x1200 monitor, however it uses white LED back light, so you'll definitely get a blue tint on your white and colors. If you have a color calibrator, you might be able to fix the color tint shift, but I don't know as well. As it uses white LED backlight, it can only do "standard" gamut, so sRGB. And it comes with a pre-color calibrated sRGB profile with report (again quick calibration). As inputs you have HDMI, DisplayPort, DVI and VGA. It uses IPS panel, however I don't know for sure, if it uses a 8-bit panel, but I have not seen any reviews that actually open the panel, get the panel model, and see if it's a true 8-bit panel or a 6-bit panel using AFRC to emulate 8-bit.  As it comes with a color calibrated profile, I tend to guess its a 8-bit panel, as I never seen a 6-bit+AFRC with calibrated profile.
 
 
After those, you really fall with out of your budget, or 6-bit+FRC (eIPS) panels, like the Dell U2412 - 1920x1200 - 16:10. Great monitor, but I don't think you'll like the panel. And of course, all the lower end ones uses white LED back light.
 
Note:
To use 10-bit colors with the supported monitors above (for the first 2 I mentioned), you need to use DisplayPort, with no adapters or converters, and of course, you need to use a support GPU and drivers. You probably know this, but I just mention it for those who don't know.
 
And again for those who dont' know, FRC and AFRC,mean Frame Rate Control. This means that to emulate a color that the monitor can't produce, it picks 2 colors, and switch between them back and forth, up to the speed of response time of the monitor, to fool your eyes in seeing the correct colors. While this method is perfectly fine for most people, even here, when you need some level of color accuracy, you want a true 8-bit panel, so that the monitor doesn't need to do this.. at least not for 8-bit per channel colors. If it support it will use it for extended colors: 10-bit color per channel, for example. However, while 10-bit color per channel sounds cool to have, 99% of the content on the web, games, movies, etc, are all in 8-bit. So unless you specifically work with 10-bit colors, this feature is useless to you.
The A in FRC is: "Advance". It just means it uses a color processor and its Look UP Table to help out.

Response time is B.S value, and they tell you. You will see that they refer in the fine prints, or next to "response time", g-t-g, or "g-to-g". This means gray-to-gray. In other words, every company has it's own way to measure response time (like the actual process). Moreover, as the fine print says, the response time is the time the monitor panel takes from changing a color to another... in this case, gray to gray. But which gray? That's exactly it... nothing says that it can't even be the same gray color (see 1ms).
 
TFTCentral, an in depth monitor site, shows this, and you can see it from any of their monitor review. For the sake of example, I am showing a bit of 2 extremes to show the impact more visible. The first one, the Dell U2410, is a super fast IPS monitor, quite impressive, possible one of the fastest. It was a 750$ monitor. The other one is a BenQ is a somewhat early 120Hz monitor, so TN, which what it looks like a 60Hz monitor overclocked, and not a true 120Hz.
 
So, lets compare:
 -> Dell U2410 - true 8-bit IPS panels, 6ms response time, 1920x1200. Note: the more pixels rows the monitor has, the slower the response time, as the LCD monitor refreshes from the top to the bottom, row by row. Hence why you have tearing in a fact action scene or game if V-Sync is off. Just something to keep in mind.

 
-> BenQ XL2410t - 120Hz TN panels, 1ms response time, 1920x1080. So this monitor has everything on its side to be fast.

 
Well.. someone is lying quite a bit... I think you can see who...
 
And for kicks, here is a third example, ViewSonic VX2739WM, TN panel 1920x1080, 60Hz, 2ms response time.

 
Not very 2ms to me, compared to the 6ms from Dell.
 
So, it is important to read in depth review to get the real response time of the monitor.

The Dell U2713HM and the U2713 both uses true 8-bit panel yes.
Response time, is a B.S measurement. I explain it here why it is the case: http://linustechtips.com/main/topic/27813-acer-s235hlbbmii/?p=357440
More colors is always awesome to have... but in reality useless if you don't need it.
100% of content most people interact here on this forum is encoded in 8-bit colors. So, 16.7 million colors. Therefore, you don't get to enjoy 10-bit colors.
The U2713 is more focused on "color work" or if you prefer: photo editors, illustrator, artists, and so on, that can't afford or don't need a true professional grade monitor. It's fine for gaming, but it overshoots sometimes, which might be annoying on strongly contrasted colors, like a plane in black passing through a light blue sky. The other monitor doesn't have this problem. The backlight of the U2713H is better. It uses GB-LED backlighht, which is green and blue LED's put very close together with a layer of red phosphor to output a white light. The result is a nice white light, on the wide gamut spectrum, much like hig-grade CFL back light monitor, another costly backlight technology.
Each backlight technology in a nut shell:
-> Low grade/Standard CFL: Yellow/red'ish white to a warm white, depending on the grade. Consumes too much power, and cost more than White LED.
-> High-grade CFL: Near perfect white -> costly
-> White-LED: inexpensive, outputs a cold white or blu'ish white depending on the grade of the LEDs.
-> GB-LED: Costly. Outputs a hint green'ish white light.
-> RGB-LED: Very costly -> perfect white, where the backlight Red, Green, and Blue color intensity are adjustable.

Damn... we only have old monitors here.
ha ha ha... ok boring joke :)
Sadly you have to choose, 1440p or 120Hz. Beside you'll be limiting by your GPU in big games, unless you don't mind playing them at much reduce graphics.
Remember, that your games need to run at a solid 120fps, to enjoy 120Hz monitor. 1440p is quite intensive as it is.
You COULD get these certified/reject panel Korean monitor off eBay, where some of them can POTENTIALLY, MAYBE, if you are lucky, IPS panels overclock up to 120Hz. Many were able too, but also many failed. Of course, you wont' get true 120Hz... the IPS panel itself is not fast enough, you'll get some blur effect going, which might seam like more frame, but side by side a true 120Hz, you'll see something is strange with the IPS panel.
That monitor aside, you have to pick which is more important. Color reproduction, wide view angle, (IPS) or speed (TN).
For 1440p monitors, IPS, you have:
-> Dell U2713HM which features a true 8-bit panel, and manufacture pre-color calibrated sRGB profile with report. A profile ready to be selected once you plug in the monitor. If you wonder, Dell uses LG IPS panels in this monitor.
-> ViewSonic 2770, which is similar to the Dell one above, but no pre-color calibrated profile, but the default colors are pretty good.
-> ASUS PB278Q, as mentioned above, which is worth a look.
All 3 monitors are very well reviewed by in-depth monitor review sites.
They are better monitors, but I would need to know your budget, as they are not cheap (see the U2713H  as an example).

You are comparing a high-end consumer grade monitor vs an entry level professional grade monitor.

Anyway for gaming, the U2413 is overshooting, the NEC one has high input lag, but good response time.
The U2413 comes with 2 pre-color calibrated profiles with report ready to be select on the monitor menu: Adobe RGB and sRGB. However, the calibration is a quick one, and inadequate for professional usages. Beside, a calibration needs to be at least 2 times a month to compensate for the wear level of the backlight and panel for color critical work. NEC monitor, like all pro grade monitors assumes you have a color calibrator, so they don't really bother.

The NEC uses high-grade CFL to output a true white light, giving excellent based for all other colors. The U2413 uses a new backlight technology called GB-LED, which is green and blue LEDs put very close together with a layer of red phosphor to output a white light. The downside of this technology is that the light output is a hint too green. (While LED, the standard tech on lower end monitors, is too blue). The best backlight technology, if you wonder, is RGB-LED, where you have red, green and blue LEDs puts very very close together to output a white light, and you can adjust the intensive of each color to calibrate the white backlight perfectly.
Of course, not cheap.

The ideal monitor for you is the Dell U2410. It has better response time, similar input lag, has game mode to reduce the input lag a bit further, high grade CCFL backlight, 1.07 billion color support. 16:10 - 1920x1200 of course. It's like the monitor fits in between the that you have selected. Sadly, the monitor has been discontinued, so it will be hard to find. This is what I use.

NOTE:
No mater the monitor you pick, for 1.07 billion colors support, you need to use:
-> DisplayPort with no adapters. I don't know about the NEC.. it MIGHT support via dual-link DVI, but the GPU also needs to support it.
-> GPU supporting 10-bit colors (All GeForce 200 series and newer, with DisplayPort, support it. I don't know about AMD, you need to check.)
-> And of course, 10-bit content. All content everywhere is in 8-bit, to fit 16.7million colors monitors, which is the most popular.

I have never tried 1.07 billion color support with my monitor.