What is your video card? There are two primary standards, HD3D, and 3D Vision (2). Depending on your video card, your choices are much different.
I don't know how well Bioshock Infinite will be, but BioShock 1 & 2 are only listed as "Good" in 3D, which means there are a few problems.
Skyrim is "Excellent", and from personal experience, it is, but water is poorly done when you can see items in side it. That can be mostly fixed with a mod, but it only works with Nvidia's 3D Vision version of 3D:
http://helixmod.wikispot.org/gamelist
SWTOR is listed as "Good" stating some objects may appear at the wrong depth. Sometimes that just means the UI is at the depth of the monitor, which isn't a problem, other times it's a bigger deal. If you are trying to be competitive, 3D is not normally an advantage. 3D looks amazing and more life like, but it also makes it a little harder to aim.
All 3D monitors are TN panels, if you plan to go with active shutter glasses, which are generally the best for gaming. TN panels will never be considered "Great" at color reproduction, but they are great in response time, and 120hz monitors adds to that since images get updated twice as fast.
The ASUS VG278HE is probably the best, but you will have to buy a 3D Vision 2 kit to go with it. What is special about this monitor is it has a 144hz refresh rate, which means you can get to 72 FPS 3D gaming, while normally 60 FPS is the cap.
The ASUS VG278H is 120hz, but has the emitter built in and glasses come with it. It's probably the best 27" 3D Vision 2 monitor other than the one above.
The BenQ XL2410T is considered a great 23" 120hz monitor that also supports 3D Vision 2, but not built in. You need to buy the kit separately.
The BenQ XL2410TX is the same as above with a built in emitter and comes with glasses.
For AMD systems, I'd recommend the Samsung 700, 750 and 950 monitors. They will not support 3D Vision, but they do support HD3D at 1080p @ 60hz per eye. The negatives are these can be a bit dark when playing 3D games, unlike the 3D Vision 2 versions.