If you are new to electronics, but want to start making things with Arduino, I recommend that you begin with an Uno and these great resources.
- Make’s Getting Started with Arduino book
- Make’s Ultimate Arduino Microcontroller Kit
The book includes a brief introduction to electricity and then dives into working with Arduino.
The kit includes many of the things you will want to play with as you read the book and includes an Uno.
Once you have a handle on the basics, you can add internet connectivity with the Arduino WiFi Shield or step up to the Yun.
The WiFi Shield can be used easily with the Uno, but it will limit the amount of memory and the IO pins available to you. The Yun avoids these limitations, but has some frustrating idiosyncrasies to it. Because of these idiosyncrasies, I don’t recommend the Yun for beginners.