All ARM core architecture designs are owned by ARM, Ltd which in turn licenses these cores to manufactures whom combine the ARM core with various peripheral modules to produce a complete microcontroller.
ARM Ltd's tight control of the core design ensures the functional elements of the core and its associated instruction set(s) remains uniform regardless of the manufacture of the actual microcontroller.
While the nomenclature for a register, timer, etc within a specific compiler, header files, etc, may vary from one manufacturer/programming platform to another, the basic functionality of a common ARM core remains the same regardless of the manufacturer or programming platform.
The uniformity helps facilitate a programmer/designer the ability to migrate from a microcontroller of a specific ARM architecture manufactured by one company to a microcontroller of the same ARM architecture produced by another.
Currently the ARM Cortex-Mx series is quite popular, many manufacturers of ARMs offer a line of Cortex-M0, Cortex-M3 or Cortex-M4, including Atmel, TI, NXP, STM and others.
There are numerous relatively inexpensive development boards available which feature the Cortex-M3 series, several for less than $10 USD.
STM32VLDISCOVERY
STM32F3DISCOVERY
Olimex Atmel ARM Boards
Olimex NXP ARM Boards
Olimex STM ARM Boards
Embedded Artists NXP Development Boards
The STM32 Discovery line of development boards are an excellent value for your money, as these boards typically include a JTAG programmer/debugger which is compatible with several programming platforms including KEIL MDK-ARM compiler and uVision IDE.
If serious about learning and programming any of ARM series, you will want reliable JTAG programmer/debugger hardware, unless the development board provides a dedicated JTAG programmer/debugger.
I own several Segger JTAG programmer/debuggers which can be quite expensive, however they do offer an educational version of their JLink, essentially the same as their professional version for approximately $50 USD, a fantastic deal:
Segger J-Link EDU
Hope the info helps you in your endeavors,
BigDog