I have NO experience with using a TV for a gaming monitor. I have a home theater setup with a 100"+ screen I use for surfing/etc, but only have tried games like Starcraft 2 and Aces High, and with AH only to pop in to check out the arena numbers and see who is online.
I have however used triple monitor setups as many here have - if you can afford it, it's an option you should at least check out, try and see one in a store or PC enthusiast shop if you can, or whatever. You can choose some pretty high end monitors, but as stated, need some horsepower to run them.
I cannot state enough that of all the options to make a gaming PC monitor "good" for gaming, 144hz refresh rate, or at least 120 (144hz is more common) makes the best difference IMO in terms of how games play. They allow up to 144 fps in many games, and it just looks better - many here who use 144hz monitors agree, and have posted about it in past threads this year.
1440p or 4k - I have one each of both, a 144hz 1440p monitor, and a 4k Acer - I honestly find that with most games, 1080p is fine, and works well - the difference between 1080p and 1440p in gameplay is there, and really noticeable in 4k, but for Aces High...I just prefer 1080p size resolutions for the size of the targets and whatnot.
There are some options nobody has really mentioned much here, sort of an inbetween of 3 screen and a large TV. Again, I have zip experience with TVs, but what I've read, they lack the capability to go to 144hz, which as I said, is likely the most important thing in a true "gaming" monitor, more than resolutions of 1440p or 4k, and more than Gsync (I have monitors with this feature, and while decent, isn't a must have IMO). Widescreen monitors like below might be up your alley, and there are 144hz options. Below are a couple examples.
