Minimal ARM circuit requirements
Are you sure you want to do this for a Cortex-M4? It's a big leap from AVR, and I don't see how you would make use of all the features it provides. To start with a Cortex-M4 usually comes in a large package, typically more than 80 pins for the entry level parts, and 200+ is not an exception, think QFP or BGA. Are going to make a breakout board with two rows of 40 pins to breadboard? 

The Cortex-M4 is also designed for high-speed: 120 MHz to 200+ MHz typically. OK, you may not need to design your PCB for those speeds if you use an on-chip PLL. But what about the peripherals, like USB or Ethernet? 

Of course you can run it at lower speeds, and leave out much of the on-chip functionality, but I wonder what's the use of a Cortex-M4 to start with. I think a Cortex-M3 or even -M0 is more appropriate to start with. I don't want to discourage you, I want to remain realistic.

If you do want to go ahead with the Cortex-M4 you can do with minimal external hardware. The NXP LPC407x for instance has an internal RC-oscillator which is the default oscillator at reset, so you don't even need a crystal. A reset circuit and proper power supply decoupling will be all you need to get it up and running.  

For a Cortex-M0 the NXP LPC111x may be worth having a look at. Granted, it doesn't come with lots of memory, but it's available in a DIL-28 package, which is a rarity for ARMs. Alternatively you can use a development board like the LPCXpresso,

  

where the right half is the application board, which can be separated from the LPC-link. As you can see there's hardly any external hardware required for the application. And if you solder a set of headers on it you can plug it onto a breadboard.