Fedora or Redhat would be the most user-friendly, IMO. They install eaily and come bundled with GNOME and/or KDE, which are desktop managers (give you a nice windows-like interface). If you use a window manager/desktop manager with a small footprint, chances are it will not be very easy to use.
However, I think that Fedora will be managable (note.. MANAGABLE, not fast) on your machine. Good enough for learning linux. For comparison, I installed Fedora on my OLD box (180 mhz, 96 mb ram, 4 mb video, you get the idea, this machine doesn't even ahev a USB port!) and it is slow, but still usable. However, NT 4.0 ran a lot faster on the same machine.
Note that it's the desktop thats slow, not the Linux kernel. So using a simpler window manager (check out IceWM and Ion) will make it run a lot faster.
As for the downloading, for a minimal fee (like $7) there are websites that will mail you all the linux cds.
I hope this was not too much of a ramble.