Teensy 3.1 is a Arduino "like" system that can do all that with libraries that are already written. It runs at 96MHz and has audio functions that use the DSP of the chip. It can do stereo high quality audio. It is also significantly smaller than my thumb.
Edit:
There is also an audio board for it that includes SSD (small flash card) that is fully integrated into the libraries.
The Teensy 3.1 is a 3V3 device with 5V tolerant digital inputs but the analog pins are 3V3 maximum (this might complicate connection to the accelerometer if it is a 5V device).
It does not have a 5V output pin. Its DC input must be 3.7 to 5.5 volts so if you supply it with 5V that can also be your 5V supply to other devices. It does have a 3V3 regulated output @ 100ma maximum - the audio board also uses this which will reduce the 100ma but I don't know by how much.
The audio board has a headphone jack and a uSD socket already populated. If you need a volume control pot or access to the line-in or line-out pins you have to add those yourself.
There would still be 4 free ADC input pins and several digital pins free on the edge of the Teensy 3.1 board when the audio board is connected but there are several others, either as through-hole pins in the interior of the board or as pads on the bottom of the board.
If you are unsure of anything it would be best to ask in the Project Guidance forum at: