I am not sure if I am in the right place. I would like to build a device (as small as possible) that has an accelerometer and can talk to my phone via bluetooth. Im not asking anyone to build this for me. I would just like some starting help. Can you tell me the parts that I would need to accomplish this?
Your smallest solution would not involve a conventional "Arduino" at all, but rather something like an nRF51822 Bluetooth Low Energy chip/module, which in addition to being a radio is a processor in its own right capable of running custom software built in a variety of ways, including one that extends the Arduino IDE to support it.
Basically, you need the nRF51822 or similar chip, an accelerometer, and whatever solution for powering the two you decide upon.
In terms of conventional bluetooth vs. BLE the choice depends not only on technical merits, but also on which phone you want to connect to. If you want to connect to an iphone, you are basically locked into BLE as the bluetooth stack there is restricted to approved devices. On the other hand older/cheaper Android devices may not support BLE, or support it poorly, while their conventional bluetooth does not have the approval restrictions of iOS.
If you want Arduino programming AND you have physical size limitations, you may want to checkout RFDuino.
They have a variety of breakout boards that make rapid prototyping easier.
I should say however that while I have purchased one of these, I have yet to get around to using one. Others with more experience may want to chime in.