I would definately reccomend an ATI Radeon to you. I know that there are lots of people that say that ATI is crap compared to Nvidia. ATI doesn't have good support or drivers. However, they do provide better image quality then the Geforces and still pump out reasonable frame rates. The Radeon is even hardware equiped for Microsoft's DirectX 8.
On top of this, the Radeon family has hardware MPEG2/DVD playback. Just put a cheap 70 dollar DVD drive in the system and you have flawless DVD quality. For the TV out, you will need to get either the ATI 64MB Version or the All-In-Wonder Card. I have the All-In-Wonder card and it works great after I installed the latest drivers for my motherboard.