monitor or hdtv

I would go for the HDTV depending on how far away you plan on sitting from the TV. I suppose you'll be playing FPS games so I'm sure you'll have some type of wireless gamepad; just be aware that there could be some games that might not like wireless controls like FarCry which cannot be played with a wireless mouse.

For me it is simple I have two computers, one at my desk and an HTPC connected to my SDTV (haven't bought HDTV yet). I tried playing FarCry on my TV, but see my comment above. Halo worked fine. I mostly play strategy and RPG games that requires a keyboard so playing games with my HTPC has been limited; especially since it is almost 5 years old and is about to be replaced.

The only drawback could be if you want to surf the net and watch TV at the same time. You could probably do a split screen if the HDTV is capable of doing that, but that would be annoying to me.

A TV Tuner card is great, but be away that it will not decrypt any encrypted TV signal. To watch encrypted signal you would need to connect it your cable or satellite box for the signal to be decrypted, then passed though to the video card, and then to the HDTV.