Firefox 3.6.19 is compatible with Windows 2000; check out the requirement for Firefox 3.6.x:

• https://www.mozilla.com/en-US/firefox/3.6/system-requirements/index.html

Firefox 5 (current version 5.0.1) is also compatible with Windows 2000:

• https://www.mozilla.com/en-US/firefox/5.0/system-requirements/index.html

Always download Firefox from one of these sites:

• Current version: https://www.mozilla.com/en-US/firefox/fx/
• Current version (choose language and OS): http://www.mozilla.com/en-US/firefox/all.html
• Other supported older version (choose language and OS): http://www.mozilla.com/en-US/firefox/all-older.html

Just a reminder: Windows 2000 is no longer supported by Microsoft and may contain un-patched vulnerabilities.

Windows and Linux didn't get the 3.6.19 update, it was for Mac OSX patches. The main download servers (vs the update servers) only handle the same version of Firefox for full downloads, so the Windows and Linux version of 3.6.18 was re-labeled to 3.6.19 to satisfy that requirement. So on Windows and Linux the 3.6.18 and .19 version differ in version number only.

Firefox 3.6.20 will be released in a few days (Aug 16), so you can also wait for that to avoid updating twice within a few days.

• https://wiki.mozilla.org/Releases/Firefox_3.6.20

Is there some explanation why the download of 3.6.18 is over 11MB whereas the download of 3.6.19 is between 8 and 9MB?

Where are you coming up with those file sizes? Are you comparing an exe file to a mar file? from here - http://releases.mozilla.org/pub/mozilla.org/firefox/releases/

ftp://ftp.mozilla.org/pub/firefox/releases/3.6.18//win32/en-US/ - 8409kb
ftp://ftp.mozilla.org/pub/firefox/releases/3.6.19/win32/en-US/ - 8404kb

I'm comparing the size it said the download was when I clicked on uipdate (and I bailed out, choosing not to tie up the line for 45 minutes or more), and the size of the downloaded .exe on my Flash drive that I brought home from the library.

Best is to wait a few days and wait for Firefox 3.6.20, to be released on Aug 16 if all goes well.

• https://wiki.mozilla.org/Releases/Firefox_3.6.20

Depends on when I'm next at the Library with a Flash drive - on the Win2000 I get 4 minutes per MB; on the WinXP it's 3 minutes per MB but I only turn that on once every month or two to update WinXP. Since the Library has a T-1 or T-3 line (not sure which), it is virtually instantaneous.

It you are on dial up then it is important not to miss any minor updates, because minor updates are small files compared to a full update.
It is even better not to do a full update to another major version, but to download the full version of the next release and install that version, because that may save you a few MB (full version is packed more efficiently than an update .mar file).