1.Do starting with Cortex-M4 is good idea? (because of ARMv7, Harvard mem arch etc)
Yes, why not? If you are programming in C language, I think you won't feel the difference (only the compiler will). In the other hand if you are programming in assembly, then there are differences of course.
2.between NXP, ST and TI Cortex-M4 based MCUs which is better for start? (based on requirements above)
From those MCU, I only know the TI Tiva MCU. You can buy the low cost Tiva C Series TM4C123G LaunchPad. This Launchpad has two MCU on it. One of them functions as the programmer and you could use it, if desired, to program/debug an external Tiva C MCU.
You can use an Arduino-Like programming IDE called Energia to program simple applications very quickly. For complex applications, you should use Code Composer Studio (CCS), which is free under certain conditions (one of them is using it with low-speed programmers as the one in the Launchpad). Current CCS (version 6) allows to easily install libraries and examples. Free libraries that allows to "easily" (this is of course relative) work with peripherals inside the MCU, interface with external peripherals, or having a RTOS (real time operating system).