Picking a bluetooth module
BT modules usually have at least one of the following interfaces: UART serial (most common), SPI, I2C.  These interfaces are standard, and agnostic with respect to controller brand and model.  LPC1313 (which was mentioned in the O.P.) has all of these interfaces.

P.S. For something like a BT remote for changing music on Androind, consider looking for modules, which can support Human Interface Device profile (HID, graphic details here).