I'd seriously consider downloading ZDoom, then hitting Steam and buying Doom, Doom2, and the other oldies in a "value pack". There, you can rip the original WAD files and drop them in the ZDoom directory. This gives you a decent engine, plus the content of Doom/Hexen/Heretic/Doom 2.
Tude - ANY video card would be able to run Doom now. I have a 5 year old computer with onboard video that can play it. Even if you can't play the browser version above, the video wouldn't be the problem - remember Doom is 16 years old now.
zDoom or Doomsday have put a lot of work into updating the graphics.
Doom pack on Steam is 39.99 Steam For all the Dooms including 3. Or 69.99 for the Quakes, Hexen, Heretic, Commander Keen, Wolfenstein etc.