Using IMU for a small Arduino and bluetooth support
If you're new to Arduino I'd suggest avoiding the Mini and the BULLSH-fun that external programmers bring. 
Something like the Pro Micro is much easier, almost as small, and less likely to bite.

Often the best way to pick hardware is to look for a tutorial (like This one) before deciding what to buy. While I personally haven't used IMUs it looks like the "6 Degrees of Freedom IMU Digital Combo Board - ITG3200/ADXL345" from SparkFun would be (relatively) easy to use.

I've used the RN-41/2 Bluetooth modems (the same as are found in BlueSMiRF modules) and usually gotten on OK with them. There are plenty of tutorials available with a bit of Googleing.

Adafruit do a good line of Lipo batteries and chargers. They also have wireless charging modules if you're looking for extra brag-factor.

Hope this helps.