Low cost DSP development kit
You can do a lot for "free" by working with python/numpy.  You can work with .wav files.  Most computers have some kind of sound proceseeing hardware for audio I/O, but you may want to get a sound card if you're computer doesn't already have this.  You can record audio for processing using Windows Sound Recorder.  Numpy has tools for importing and exporting .wav files.

If you really want to learn about DSP coding, get a development Kit from TI or Analog Devices.  These kits include a board with DSP, computer I/O (often via USB) and development tools for generating and debugging code.  Analog Devices seems to have the least expensive development kits.  Try something in the EZ-KIT family from Analog Devices.