Best Linux Distribution (for a small screen)?

[techhelpbb]

There's lubuntu:
https://wiki.ubuntu.com/Lubuntu

With 512MB of RAM, you don't need to worry much.

The default "Desktop" installer requires 384-800 MB of RAM (depending on selected options.) If you have problems, please use the "Alternate" installer.

I've seen that installed on 2GB of storage and how much it needs will depend on what you install.

If you can't get your desktop or window manager to detect 640x480 boot in text mode and modify the xorg.conf to use the VESA driver. Just exactly what you need to do depends a bit on your choice of Linux. I will spare you an explanation of the good old 'modeline's.

There's also Puppy Linux (as noted above):
http://puppylinux.org/wikka/MinimumSystemRequirements

I've seen that installed on 512MB.

Of course there's actually ThinStation:
http://www.thinstation.org/

Which is basically Linux for a thin client (there are other choices for this but it's not clear to me you want a thin client as much as resource challenged Linux computer).

I will refrain from sending you my Slackware book. At some point 'back in the day' 32MB of RAM and several hundred MB of storage would have been 'excessive'. In that retro 8bit gaming sort of way.

I wonder if you really need a GUI (graphical user interface) or if you could get away with using 'curses' for a TUI (text user interface). If you did you could get this down to less than 2MB of storage and around 8MB of RAM. For example:
http://reboot.pro/topic/5796-linux-on-a-floppy-disk/