It's a tough call Fugi, one I just made recently as well. I was either going to get one of the new hi rez 2560x1440 27", or 3 monitor setup. After reading that the 2560x res monitors don't perform that great with games in mind, I went with the 3 screen setup, and got 2 matching 23.5" Asus LED cheap-o's that match the current cheap-o I had. They were on sale as a bundle, two for 259$, which was about 100$ off. I'm not sorry I went this way at all, but I'm in your boat as well regarding TrackIR.
I can't decide if I should switch to it. I really would like it with DCS stuff I think, but AH I'm not so sure. Shooting is my concern, like yours, and if there is a button you can program to completely turn off the TrackIR system and revert to normal front view instantly, I would do that (semp, maybe you can clarify that a bit for me). Freely looking around while not in combat would be fun, but in combat I'd like that option to go back to a steady, not moving or out of line, front site picture of the normal cockpit view as it is without TiR.
Anyhow, I'd vote you go with 3 screens, it'll likely be cheaper, unless you buy a 300$ stand, than getting a new 27" hi rez or 32" 1080P TV, which would be around 400$ I think, for a low end 32" LED LCD TV. I paid 325$ recently for my mothers 32" Toshiba LED LCD but it is only 720P, so I'm just guessing on that price. As far as the view, you'll rapidly get used to having the other 2 screens, and will LOVE LOVE LOVE it, in lots of other games besides AH as well. COD, Skyrim, BF3..they all look amazing in 3 screen. Just remember, you're going to need some serious GPU horsepower to run those games at max res/ultra settings. If you just are worried about AH, a mid to lower-high end video card will get you by in 3 screen, so long as you don't need every single thing cranked to the max detail/resolution/FSAA wise.
Good luck, post some pics with whatever you end up getting!