Minimising the siren noise (cost effective TI processor)

This is a very broad question. You could have a dozen constraints that factor into your choice of DSP. And TI has a very broad range of DSPs that could fit your needs depending on those constraints. Cost, audio sample rate, number of audio channels, on-chip/off-chip ADC & DAC, fixed vs. float, MIPS requirement, power source, power limitations, those are some of the constraints.

The easiest recommendation is to move forward with the DSK that you have in-hand. Develop your algorithms and do a proof-of-concept. If the ADC/DACs on the DSK are adequate, then you can easily make decisions later for what you might want to go to production with for both the analog interface components as well as the DSP.

A more recent DSP like the C6748 may be a good choice, too, or a fixed-point DSP like the DM6431 might work for you if you do not require the floating point capabilities, but it is usually easiest to develop an application using floating point. Migrating to fixed point later could save you some cost but might require some additional development time.