Dell makes TNs, too...but I don't know of any good gaming monitors from what they make that is TN.
Of those, the U2414H, U2415H, or P2414H (reading between the lines, here). The P2414H is nearly the same, in terms of panel, as the U2414H, just matches sRGB, where the Us match Adobe RGB (a non-issue, and some games are tweaked for sRGB to the point that using the 'standard' Adobe setting will look greenish, so you'll want to use the sRGB preset on the Ultrasharps, anyway), has a USB 2.0 hub, not 3.0, and has DVI input, for less money (my favorite monitor of the last year). The U2415H is taller, which really won't help in most games, and may even be a problem in some games that have hard-coded 16:9 stuff in them.
The 2412 and 2413 monitors have a pretty heavy anti-glare coating, almost looking like wet cloth over the monitor, sometimes. OK for office use (and, the '12 has a better panel, in terms of angle and color, than the '13 or '14 models), but not anything I would spend my money on for home. The 14, and now it seems 15, series AH-IPS monitors have a much lighter AG coating, and are very fast responding, at slight cost, relative the older ones, in viewing angle and color vibrance (noticeable, with multiple generations of them at work, but a minor nitpick, if you're not doing graphics work).
TN panels shift color more (and differently, eventually inverting) than IPS when changing viewing angle, but don't exhibit the diffuse "glow" that IPS do, and can be faster (with modern IPS panels, just don't game pitch black darkness, and the glow will be minor to negligible, however). Very few 8-bit TN monitors exist. While dithering for an extra couple bits kind of works on common 6-bit, it still leaves the panel with missing colors (there are colors that you simply will not see on a 6-bit panel, that you will on an 8-bit--what they are varies by monitor, though). The few monitors using 8-bit TN panels are not cheap.
There are cheap 6-bit IPS (e-IPS) panels, but they have more even coverage, so while they lack a little accuracy, you don't notice the missing colors phenomenon so much. They aren't too desirable, now that LG and Samsung have both been pushing down the prices of 8-bit panels, though (none of this really affects your purchase, but is just here to round out the information given).
But, TN can be fast. Very few IPS panels are good enough for 120Hz+ refresh rates, for example. If you value color over having the very quickest response, the AH-IPS Dells are very good for the money; doubly so if you also do non-gaming stuff on them for any length of time. If you want the fastest smoothest FPS experience, though, they won't be as suitable as any number of 120+Hz "gaming monitors" (I'm ignoring G-sync and Freesync, assuming the OP wants to stay in budget and buy soon). You can't have everything.
If you get one of the Dell AH-IPS, watch out for a yellowish backlight. That seems the be one of the few things that slips through the QC cracks. The backlight should look a neutral to cold white, depending on ambient lighting (if daytime sun is lighting the room from a nearby window, it should look "pure" white).
<- plays games on a Dell U2414H