The answer is one video card. IF it has "TV out", you can do TV and computer monitor on one video card.
I have been a fan of the ATI "All-in-Wonder" cards for some time thru several generations of them. Many All-in-Wonder cards use the same video chip as their non-TV capable brothers. If you do not need to record video nor use your computer as a TV, then there are some cards by ATI that do have a "TV out" but not TV in. These would do fine as well if you only want to play DVD and games on your TV.
Personally, I run the original All-in-Wonder 128 which is an earlier version of the video card you mention with no problems DVD wise. Considering your CPU speed, picking up a used earlier verion of the all in wonder on Ebay is an option.
If you do not really want/need to view your DVDs and games on your TV, there are excellent ATI cards such as the ATI RAGE 128 (with DVD in the video card) that will do the job on your computer monitor very nicely at a better picture quality than the TV. ANY TV supported image will not be as good as your computer monitor even at the same pixel count. The limitations of most TVs are the problem.
Also, be aware that the "TV OUT" are different between North Amercia and the European PAL standard. Be aware of the TV broadcast standard in your area or you could get at "TV OUT" that is not correct for where you live. That is especially true for the TV tuner "All-in-Wonder" cards.
Every working computer must be improved .... or replaced ...