nethanger1:
Is there any manufacturer you would recommend?
If you want to use a small computer rather than a powerul desktop computer or laptop then maybe one of the new, fast 'small ARM devices' that are intended as low-cost general computers rather than real-time hardware controllers would suit.
For example Cubieboard which has a 1G ARM cortex-A8 processor, 256KB L2 cache with 1GB DDR3 @480MHz. Note however that it doesn't have I2S which you may well need for fast audio-rate ADC and DAC. The computing power on that is reasonable for a small device, a lot less than a current desktop machine, but a lot more than an Arduino (including Due).
To learn about audio DSP, the DSP forum on KVR is a good place.