Best choice in ARM Cortex series for running RTOS A-,R- or M?
Cortex-M can be used for hard real-time applications, and tend to cover the lower end of the performance scale (but still a wide range).

Cortex-R are specifically designed for high performance and real-time applications (automotive, storage, modem, etc.)

Cortex-A are designed for running OS like linux, as efficiently as possible or with high performance - so determinism is not a design constraint.

Depending on the performance you need, and the particular OS, either Cortex-M or Cortex-R might be suitable for your application.One key point to check is the memory-management requirements of the OS (MMU or MPU).