This has nothing to do with the distro; it is how the kernel is compiled. You can install pretty much any distro with a kernel lower than the processor you have and then install a kernel optimized for your architecture.
i386 is for a 386 or higher
i586 is for an early pentium (i forget if a its for a P1 or P2) or higher
x86 (or x86-32) will work with any pentium or AMD.
i686 is what you want, i think, it is for PIII, PIV, Celerons, etc.
You do not want PPC (for macs) or anything ending in -64 (64-bit architecture).
I would recommend you install debian sid or ubuntu (they will both install i386 kernel) and then use the synaptic upgrade manager to upgrade to the i686 (which will make things much faster). Do not remove the old kernel right away; rather, the new kernel should add an entry to your grub/lilo menu on start up. reboot and select the new kernel, and if everything works then remove the i386 kernel.
If you go with ubuntu, do not forget to check out the site www.ubuntuguide.org to get things up and running.
Welcome to linux and good luck.
In deciding which version of a distro relates to my processor. I have a 32 bit pentium processor running at about 1.8 ghz.
i see stuff like i586 , x86 , PPC, X86-64, X86-32
( http://frontal1.mandriva.com/en/downloads/mirrors )