The simplest ruleset is Hong Kong Old Style (HKOS). It has simple scoring and very few special hands. Other forms may have few special hands but complex scoring - or simple scoring but many special hands to learn - or complex scoring and many special hands to learn (like American Mahjong).
If you want even simpler rules, have a look at these ultra-simplified Chinese rules. They even omit Kan and most of scoring, so you can understand and explain them in a few minutes. From experience I would say they are a good way to start. Once you got the basics, you can gradually add more rules of the HKOS set, and eventually also have a look at other rulesets.
One thing I especially like about the ultra-simplified rules is how scoring works:
Whoever won gets a chip or a coin from
everybody. Or just use the "ooh and
aah" method. When somebody wins,
everybody goes "ooh." You can keep
track of score on a piece of paper
too. Make a tick mark next to the
winner's name. Whatever works for you.
If you want to make things really
exciting, award an extra chip, coin,
or "aah" for a pung of dragons or
If you want to recognize dragon or
wind pungs for all players (not only
for the player who goes mah-jongg),
you can do that. It might be possible
for a non-winning player to get a
higher score than a winner, if you
allow this. But that's OK, if you like
it that way.