Autonomous bluetooth 4.0 Low Energy bracelet

Hi, My project is to make a bracelet linked to my phone via Bluetooth Low Energy (BLE). I'd like to swith a LED on or vibrate a tiny motor (examples). I need the bracelet to be autonomous (of course), with its own battery.

My idea : a BLE module, a LED, a phone. Quite simple isn't it?

Yet, i have no idea of what i should buy as BLE module... Do I should buy a BLE built-in Arduino (like RFduino for example), or a separated BLE module sewed to a LilyPad (I mean, a tiny arduino). In this last case, what type of module should i buy? Where?

Thank you for your time and your advice. Chris