Hmm well, linux is just at version 2.6 yet, I assume you mean version 8.2 of a particular distribution?
For starting out Mandrake (mandriva now) is a good choice, but a word of caution, with 64MB RAM, Gnome or KDE based distributions (mandrake, fedora, suse, ubuntu ... heck most of them) will be a little slow with 64MB RAM
out of the box. You can, of course, switch to XFCE or a light window manager after installation, but if you want good performance out of the box, look at something like
Vector Linux. It comes in two editions, the standard edition is a small ISO which has a nice and compact collection of software to get you by. Or you can go for the SOHO edition, which uses KDE (optional). I recommend the SOHO edition as it is newer and has some really good improvements.
This distro is optimised for slightly old hardware, so it will run quite fast indeed. Now Vector is easy to use, but it doesn't do too many things automatically, unlike mandrake, but with good documentation and graphical admin tools, you can figure out how to configure your system quickly.
i586 & x86_64 refer to processor architecture. i586 is basically the pentium architecture, your pentium 3 is i686, but it is fully compatible with software built for an i586. x86_64 refers to the new 32/63 bit AMD & Intel processers out there.
Finally, I hear the official pronounciation is Leee-nux, but call it what you like
