You may want to look at the contents of some "Starter Kits" to see what others have found important. There's a comparison here:http://arduino-info.wikispaces.com/StarterSetsComparison
You will find my prejudices after 3 or 4 years messing about with this stuff in the "YourDuino" Kits.
With a young person involved, where breadboards can be fussy and connections are sometime unreliable, you may want to consider "Electronic Bricks" which are small circuit boards with a connector and cable that plugs directly into a Sensor Shield (http://arduino-info.wikispaces.com/SensorShield
) or a Arduino-compatible that has added 3-pin connectors like: http://yourduino.com/sunshop2/index.php?l=product_detail&p=225
Look at the http://ArduinoInfo.Info
WIKI for cable/connection information: http://arduino-info.wikispaces.com/Cables
And you may be able to use the "Hands-On-Arduino" How-To pages at: http://arduino-info.wikispaces.com/YourDuinoStarter
It includes sample Software Sketches for most of those components.
Let us know how you do, and if you ever want to write up a "Really Young Person's Arduino How-To" i'd love to publish it on ArduinoInfo.
DISCLAIMER: Mentioned stuff from my own shop...