This thread has a good breakdown of the pros and cons of the different LCD panel types. TN is the most common because they are the cheapest to produce. They have the best pixel response times, but the viewing angles can be restrictive and color reproduction is poorer than the more expensive panels. I would like to point out that on my TN panel the viewing angle is really good: I can see up to 150 degrees to the side before the image starts to darken.
IPS has the best color reproduction, but slower response time and poor contrast ratio. PVA has the slowest response time, but the best viewing angles and contrast ratio (however some people say blacks can overpower details). S-PVA halves response times so they are just a little slower than TN, but to do so it uses overdrive which can introduce ghosting.
As far as the resolution goes, 1366x768 is native because of the dot pitch. Any resolution lower or higher will be scaled to the dot pitch because it is restricted by the number of pixels in the screen. Lower resolutions will appear blocky and blurred, while higher resolutions will appear fuzzy. This isn't necessarily a problem if you're sitting further away from the screen. For your application however, it may be a problem. You may want to find a place that will allow you to test the screens so you can see the performance and quality differences yourself. The nature of LCD screens means that whatever the native resolution is the picture quality will be spot on when running it.
A 50"+ screen is very large and may be disorienting and painful to play on if you're sitting less than ten feet from it. Combine the use of two other monitors on the periphery it will become overwhelming. You may want to consider looking at 32"-37" monitors instead. This is just my opinion, and you'll want to look at all options yourself to see what's right for you.