I have an 8300 at work from 2003 that is about to be retired (about time), although, it has been upgraded to 2 GB. The video card is Nvidia FX5200. I don't know if any proprietary nvidia drivers support that 10 year old card any more, so you may be stuck with the default nouveau driver. It might work best with a 12.04 version (maybe Lubuntu which is lighter). I know that graphics seemed to slow down in 12.10 with the nouveau driver even with a faster graphics card, but I don't know how 13.10 compares because I only have that on a laptop with nvidia GTX 765M (along with Intel graphics).

My old PC at home from 2004 with Athlon64 3200+ (2 GHz) w/2 GB RAM originally included FX5200 and I had to upgrade the psu to handle a faster video card (currently a legacy ATI Radeon X1300). It still has Ubuntu 10.04 on it, but 12.04 iso on USB stick seems to work fine on it, so I should upgrade it one of these days and give it to my grand nephew twins (they currently have Ubuntu based "Qimo for Kids" on a Pentium 550 MHz).