The later versions of 1.3 have security fixes, which are relevant if you are sharing the servers. I expect 1.3.10 to behave the same as 1.3.7, but no-one has explicitly tested it with the procedure and updated the page yet.
The wiki-on-a-stick procedure sets the servers to local only, which reduces the scope of threats considerably.
1.4beta6 also has security fixes, does not have the empty page bug, and allows the Monobook skin to be used with PHP v5 (which is the version in Uniform Server).
If you want to run 1.3, the patch for no display from configuration is at http://bugzilla.wikimedia.org/show_bug.cgi?id=736
If you did not get a LocalSettings.php file in the config folder, then the error was different. The procedure page has a trouble-shooting section which describes the various logs available, some of which are on by default. If you can find an error message, please post it, preferably to the mediawiki-l mailing list. The freenode IRC channel #mediawiki is also helpful sometimes.
-- Zigger