Which ARM MCU family is better for beginners?
The ARM Cortex M0 is the lowest and most simple architecture in the ARM family.

Personally I learned using the FRDM-KL25z development board from Freescale although there are a wide array of options.

There is an Arduino-like environment called mBed, which is very similar to Arduino although it is for ARM controllers.  You can use mBed with many different controllers such as the Teensy and even the FRDM development board I mentioned.  

If you aren't looking for an Arduino-like environment, you can use the FRDM development board I mentioned from Freescale which has a free development environment that includes a code generator called Processor Expert.  Processor Expert allows you to specify components and communication protocols and then will generate the raw code for you.  The code is still bare-metal code and will be very similar to code you would write if you weren't using Processor Expert.

Another line that is very popular, especially among the users here at EE.SE, is the Discovery line of development boards from ST Microelectronics.

In short though, for a beginner, I would very much recommend the Cortex-M0 series.  The Cortex-M0+ has the same instruction set although it us more optimized.