Strinctly speaking, "Linux" refers to the "Linux Kernel" - the core of the OS which is the same for all distributions. What is different about the distributions are the tools that wrap around the kernel making the system usable. In general, the drivers are the same accross distributions on a particular hardware architecture; they differ by the way they are distributed, (compiled,) installed, and, to some degree, used.
More or less everything on my 5680 works because everything is supported by the kernel I use (2.6.1 or the 2.6.x series in general). As long as the kernel has the capability to properly interoperate with a piece of hardware, people can write driver modules for that piece of hardware (eg. out of the box, I can use my Radeon card as a standard VGA device; I need special drivers, however, to make use of hardware graphic acceleration).
... That is by no means complete but should give you an idea; dont flame me for ommitting details
As for the distributions, it usually all comes down to your level of expertise and the amount of time and effort you are willing to put into setting up the system. For example, you could cary a Knoppix LiveCD with you and by just booting the CD you could have a fully functional Linux system on any machine (to a reasonable extent); while this seems to be convenient, things take forever to load off the CD, etc. As an alternative, you could install Mandrake or Redhat which are very user-friendly and easy-to-use and learn, especially for Linux beginners. To go further, primarily if you want to learn at first and to really optimize your system afterwards, you could spend quite some time installing Gentoo - compiling everything from source on your own machine; this will give you a much-optimized and thus a faster system along with fair knowledge of Linux by the time youre up and running... There are a lot of threads about this on these forums as well as all over the Net; do some research - it will definitely pay off.