Here's the site I got most of my idea's from.
specthismiata.com/2008/08/03/homemade-cool-shirt-system/
I used the more expensive cooler he shows which has a seal at the top but I'm not sure it's necessary. I got the pump from West Marine but saw the same one at Walmart. My fittings are a little different than his. The thin, large bolts he talked about I used electrical conduit nuts which worked perfect. This end of the system worked fine.
The shirt itself was a bit more trouble. I used an old red bike jersey and my wife took an old red t shirt cut from the nipples up off and sewed it on leaving 1 1/2" channels. Doesn't look great but works great. The trouble came from the tubing and the compression fittings. I ordered the dry break fittings and tubing from the same place. I got thicker ID tubing thinking it would be better when the belts are tightened down plus I used compression fittings that didn't have an insert that went into the tubing. When put together the opening in the tubing was just too small to pass water with any kind of pressure. A trip to Lowes got me the right fittings and tubing and now it works great!
I'm going to add a barbed fitting in the tubing so that if(when) I have to make a quick exit I won't have to fumble with connectors, I can just bail and yank on the tubes to pull them apart. You can also get the dry break connectors with barbed ends for the same thing.
Mounting it in the car I just used some eye bolts, a few small brackets to locate it front to rear, and a ratcheting tie down. and it doesn't move.