Need advice on screen purchase - TV or Monitor

[laserbeam273]

Hi all,

I've got a $350 budget to buy myself a nice external monitor for my iMac/MBA which will double as a TV for my xbox 360. So what would I mainly be using it for:

1. Standard dual monitor (i.e. more effective browsing of macrumors Actually Xcode & tutorials would be great)
2. Second display for FCP X, would be good for previewing the project at full res while keeping the editing stuff visible (I've completely forgotten the terminology!)
3. Playing Modern Warfare 3 on my xbox

So given this, things I care about:
1. 1920X1080, anything else would be a waste
2. Low response time I suppose
3. HDMI and DVI ports are very preferable
4. Best quality I can get of course
5. Decent built in speakers

I mainly need this screen for playing MW3, the rest are just very nice bonuses. Given this, would getting a TV be a suitable option? Or would I get just as good quality with a LED monitor, and not have to stuff around with as many adapters?

I also haven't got a huge desk at the moment. Though 27" would be nice for split screen.

Any tips? Thanks in advance.