What would you recommend in terms of hardware
I would go for a Teensy 3.2 and an I2S I/O board. They have a long audio DSP video that covers playing files and changing the volume. Teensy Audio Library, high quality sound processing in Arduino sketches on Teensy 3.1
Changing the volume in software is computationally expensive and many processors in the Arduino range are not fast enough to do this. Of course changing the volume with a external pot is trivial.