If it's a widescreen tv it's probably running 1280x720 which is an HD resolution but not "full HD" 1920x1080. For it is definately not HD then it could be running 848x480.
Either way if it's not full HD then it won't take a very powerful PC to drive it, say an Athlon II X2 550 CPU with a Radeon 5770 or even possibly a 5670.
If you can provide the make and model of the TV or confirm the resolution we can be more specific.
That system includes a monitor but would be a fairly low end gaming rig.
You should aim for a triple or quad core cpu and an ATI 5750 (or 4850 1Gb) or Nvidia GTS 250 as a starting point for that resolution.
The systems on site you linked have old or low end CPU's with entry level graphics although they do offer custom quotes.
I'd see if they can do something like.
ATI 785 chipset motherboard
AMD Athlon II X4 Processor 635 2.9GHz (Phenom II X2 550 Black Edition also a good option)
ATI 5750 graphics (4850 would do but does not support dx11)
Windows 7 home premium
hdd + odd
Post what they come back with and we can refine from there to meet your budget.