Best board/shield to use for wifi/bluetooth

I am working on a project and I am not sure what is the best shield to use. Since i am a newbie and don't know programming language very well, I will do my best to explain my goals of the project. I am designing a kid's toy that is interactive from both the physical toy and also an app on a device (Android, iPhone, ect.). The purpose of the toy is for the user to take care of it (feed, pet, tickle) so its needs are at 100%. The toy will have touch sensors along with LEDs and audio that send data to the app. The purpose of the app is to give the user a display of the toy's current needs which will be represented by a range of 0-100% for hunger, happiness, ect. If possible I would also like to send data from the app to the Arduino to play music and turn on LEDs.

I realize this is a hefty project and some goals might not be possible so I'm hoping for some advice on a starting off point for a beginner. Looking at Adafruit I found a few options for wifi connections. The ones that stood out to me were the Raspberry Pi with USB wifi or the Electric Imp using Bluetooth. I also found a lot of documentation for a wifi shield to go with my Uno but cannot find the shield on Adafruit. If a wifi shield still exists that may be the best bet for me since i am familiar with my Uno and there is a lot of helpful documentation.

So to reiterate, my goal is to use my Arduino to connect with an app either through Bluetooth or wifi (whichever is easier). If a full running app is not possible I can settle for an alternative. I also want the Arduino to send information to the app (touch sensors) and also receive information from the app (play music, activate LEDs). Because there will be 3 touch sensors and at least 3 LEDs, there needs to be pins available. It is a high priority to be completely wireless and run on batteries.

All suggestions are welcome and I thank you in advance for your guidance.