I started off working with linux on puppy linux and DSL(damn small linux) because the old pentium 3 laptop I had was limited in space and ram. Puppy linux is great if you are limited in pc hardware resources, as it will run on almost any old machine and it is a decent platform to upgrade from once you get the basic hang of things. I struggled a bit getting my network up and running, but once I figured it out I managed to do everything I needed from an OS.
I recently bought an acer aspire one and installed puppy linux 5 which is a few levels up from the first distro I worked on, and even though it has had a bit of an overhaul graphically speaking, it seems the engine is still suited for older machines. If you want to fiddle with linux and at the same time experience a more refined environment I recommend Linux Mint 9. I am currently dual booting Linux Mint 9, ubuntu 9.04 Net Book Release, and windows 7 starter on my netbook and they all run very nicely.
I also recommend downloading as many distros as possible and fiddling with the live bootable versions to see which you like best.
Download Unetbootin and convert your flashdrive into a bootdisk with any live distro iso you can download.
possibly check the following distros out:
puppy linux 5
linuxMint 9
edubuntu
linuxMCE (media Centre Edition)
DSL (damnSmallLinux) - (for veeeeery old machines - super tiny linux distro! similar to windows95 regarding style and functionality...)
OpenSuse
xubuntu
arklinux
You would soon see that ubuntu is the superior distro regarding support and add-on availability, but linuxMint is not too far behind it in terms of the kind of punch you'd expect an operating system to pack.
puppy linux in this regard will be the kind of distro that would attack you with a tissue... fiddling with it would just turn you off linux in the long run. rather fiddle with MINT 9