You can start with the Arduino Uno board, that is the easiest board. You can always replace that with something smaller or bigger.
A bluetooth module could be this one: Bluefruit EZ-Link Shield - Bluetooth Arduino Serial & Programmer [v1.3] : ID 1628 : $24.95 : Adafruit Industries, Unique & fun DIY electronics and kits
The acceleration is something you have to program. You could for example update the pwm signal every 10 or 15ms.