The bare minimum you need is
- a Raspberry Pi (probably model be as it has more options)
a keyboard - go for a wired USB one, not bluetooth or Wifi - they just prove less reliable
a mouse - again, wired
a screen - this might just be your TV, or could be a computer monitor - ideally it'll need to have an HDMI connector
an HDMI cable to connect the Raspberry Pi to the screen
a power supply - Apple, Blackberry chargers work well, but there are plenty of others
An SD card
Is that what's in your kit already?
You'll also want a connection to the internet; the simplest option is an ethernet cable which plugs directly into your internet hub.
If that won't work (Raspberry Pi and Internet hub in different rooms), then you're going to need a USB hub and WiFi dongle. That's because the Raspberry Pi model B has 2 USB ports, but you now need 3 (keyboard, mouse and dongle).
Again, there's a long list of hubs that are proven to work well with the Raspberry Pi. Follow the link in Davespice post above.
That'll give you a working Raspberry Pi with access to the web.
Does your child want to do project like robotics and stuff? That's what the extras in the adafruit bundle give you.
The Pi comes with some simple games, and programming tools aimed at young teenagers (Scratch) already installed - I'd get a book if that's where your kid wants to go. I don't have any I can recommend because I don't use it, but there must be something out there - hopefully others will be able to offer advice