The acronym DSP refers to a broad spectrum of applications, ranging from trivial image enhancement, audio filtering, realtime or not, and with a CODEC or without it, being these just a small sample of the whole. In addition, there may be different levels of resolution required, which would recommend a floating-point processor of not. In shorts, say exactly what you want to do.
Still an overly open-ended question with NO ANSWER.
Use a TI DSP they are expensive (to help my TI stock go up! ;-))
* disclaimer, I don't actually own any TI stock.
Seriously though TI makes a lot of DSP parts and it's likely that you'll see their parts and tool chain if you eventually work on DSP processors in industry applications.