STM32, and want to start playing with them but don't know how or where to start; I'm here to help.
ARM is taking over the embedding wold, they're ubiquitous in smart phones, tablets, laptops, other computers, cars, refrigerators, microwave ovens, monitors, printers, you name it!
Note: Be aware that ARM is an architecture that manufacturers can implement. Is a common mistake to think ARM is a microcontroller on itself, it is not.
ST Microelectronics's implementation of ARM are the STM32 microcontrollers: inexpensive, powerful and with great free software/hardware support.
Various series are available: F0, F1, F2, ..., F7; From less to more powerful. You can identify your chip series after the STM32 prefix, I'm using a board with the "STM32F103C8" chip, so the series is F1.