Run a processor through USB
To stay within USB requirements you are allowed to use 500mA @ 5V power. This is certainly enough for the microcontroller but the display may probably need more. 

Usually the Cortex-M devices feature a little internal (embedded) flash which is usually in the size of 2MB. If you need more memory, you could attache either an SD-Card or some NAND Flash.

I'll just give an example for a evaluation board which has a Cortex-M4, a display and some flash: http://www.atmel.com/tools/SAM4S-EK2.aspx. Yet, there is no support for multi-touch, you would have to implement that by yourself (with a display that supports multitouch of course).

Prices for controllers: digikey or farnell will give you a good idea, if you are to produce more than 10k pieces you'll probably be able to find cheaper sources.