Are there any Linux distributions specifically designed for netbooks

I know of no existing distro but this should be rather simple to build with Debian using preseeding.

You Just create your own package that basically depends on the packages for your benchmarking solution. That package comes with a /etc/init.d/ script that starts the benchmarking at boot, stores the results wherever you need them and shuts the system down afterwards.

With preseeding you can automate the debian installer to just take the system, slap debian on, install your custom package, reboot, have the tests run and shut the system down.

I started to make this as a joking comment, but I'm actually going to go ahead and make it a serious suggestion. Check out Linux From Scratch, which isn't a distro per se, but rather a book and toolkit for building your own running Linux system from source, without a distro.

If you were new to computers in general, this clearly would be jumping right off into the deep end. But if you're a competent sysadmin with another OS, it really shouldn't involve too much that you can't handle. And it will give you a good, hands-on understanding of what you really need underneath the shiny KDE or Gnome hood to make the system actually work.

At the GUI level, modern Linux distributions are basically almost like Windows or OS X, but with a whole host of different conventions and oddities that will drive you crazy (until, we hope, you grow to love and/or tolerate them). And because it's put together from the work of tens of thousands of different developers, sometimes the integration isn't perfect and the underlying bits poke through.

So, consider starting from the underlying bits and see where that gets you.