I would give a big vote for Puppy Linux if I were to choose from so-called Veteran choices. It's meant to be light weight and that is exactly what it does. However, I came across a new Linux distro by the name of Bodhi and I have found it to be incredibly fast. It is quite new, currently released version is 1.4.0, but I believe this distribution has a lot of potential. Keep in mind, there are bugs and it has "maturing" to do, so to speak.
Running the Enlightenment, or E17, desktop plays the largest role in why this distribution is so fast. It will run on just about any system and I even ran it on an old laptop with 256 ram - was surprised that it ran so fast and I would say it was close to Puppy performance there! However, boot up time is not the only fast part of this operating system. Desktop response time, using various programs, browsing, and just about anything else that you can think of, was incredibly responsive. I would recommend any user that has the slightest bit of Linux knowledge to give this little system a go. I do not run in as a main OS simply because it is going to be changing rapidly over time and I do need something that is considered more stable over long periods of time. I constantly keep updated on the progress as I am eager to see where this little distribution will go over the years.