I'd try Kanotix if you say "Debian" doesn't work on your computer. I haven't found one computer it doesn't work on in two years from PIII upwards. It's Debian with better hardware detection.

I used to think Knoppix for LiveCD use and Kanotix for a hard drive install but I now use Kanotix for both. These are all developments and Knoppix was the seed for many distros to start, and improve, from the original. What is 'improvement' - for some it's Kanotix, for some it's Ubuntu etc. - both very different so defining the 'best' is difficult as peoples' requirements are so different.