A close to silent PC with a 64-bit CPU and a "quality" graphics card doesn't exist. You're going to have to deal with a bit of noise pollution (might want to consider getting a fan control as well, so that when you aren't doing anything CPU or GPU intensive, the fans speed down).

For now, I'd probably go with the Radeon 9800 Pro (it'll set you back about $200-$230).

What exactly would you be doing on your new computer. Playing games, animation, encoding?