Okay, so I got the first (very rough) version working.  To control the Peltier heating/cooling modules I ended up going with a Arduino Mega 2560 that provides PWM to an Adafruit Motor control shield.  Since peltier modules should have a constant DC current instead of PWM, I added some 47 uF capacitors to help smooth out the PWM signals.  Next week, I'll take them back to the lab at school to check to see how much good the capacitors are actually doing.  The motor control shield is handy because it controls 4 motors and does forward and reverse.  For the peltier modules forward and reverse switch which side is hot and which side is cold.

Since the vibration motors draw about 100 mA at 5V, they can't be driven directly by the Arduino either.  So I built a little board with 5 transistors on it that are used to switch on and off the vibration motors. 

The whole apparatus is powered by two 18650 li-ion cells that I salvaged from an old laptop battery.  A shot of the whole setup without the attachments to the shirt is shown below:

To attach them to the shirt, I hot glued pockets on the inside of the shirt for the peltier modules and vibration motors.  I also cut little holes for the wires to exit.

I added straps to hold the Arduino on and a pocket to hold the batteries on the back of the shirt.  When finally put together the shirt looks like this: