Please suggest a Cortex M3 controller

Are you asking for a specific device part number in the Concerto Series of devices (ie. Cortex-M3 + C2000 DSP), or just Cortex-M3 only?

This forum is associated with the C2000 family of microcontrollers which the aforementioned Concerto devices are associated with.

Also, would you provide more details on what features you need aside from a RTC subsystem?

3 Uarts

1 SPI

RTC backup

Go to http://www.ti.com/lsds/ti/microcontroller/arm_stellaris/product_search.page

Add the parameters SSI/SPI and UART category.

You can find the appropriate device with the above criteria.  There are too many to list here.