Please remember that we are all just users, no one here is paid. The Hatter helps a lot of people here, so please bear with him if his answers are short and to the point. The system references he suggested are the ones that we all know and can respond to most quickly.
As Grant says, your system is most likely a 2008 (3,1). All the original delivery video boards had two DVI ports and many have upgraded to the ATI 5770 board that supports up to three screens. The most common interfaces DVI (being phased out) HDMI (being phased in) and VGA (old school but still here.)
The current choice of monitors is wide, but it comes down to a lot of 1080 (1920x1080) monitors and HDTVs of various physical dimensions, a smaller number of more expensive 2560 x 1600 units and some (usually cheap) lower pixel count units. The choice is yours depending on your needs.
The built-in screens on your other computers are controlled by their own video boards. There may be some way to adapt them, but if it exists it's going to be far from easy.
The TV is just an HDMI device. I have one on my system that is connected by an inexpensive DVI-to-HDMI cable. Grant is correct again that a TV is not a monitor and may not be comfortable to watch in that mode. I use mine for video playback and color grading.