I would go with 1/4 inch inner diameter poly tubing, (you can get it at home depot or lowes). I cant reccomend a specific thermostat because I havent researched wich would be best for this project. maybe some one else who has made one can chime in. I do know the more coils you put inside the fridge the more back pressure you will get reducing flow but you will also make it cool the water more efficiently (50 coils will drop water temp twice as much as 25 coils will) when making the coils I would use a ventilated structure, make a basice frame work and notch where you want your coils to sit so the notches hold the tubuing in place, then start wrapping the coils around the structure leaving at least a 1/8th inch gap between each coil to allow air flow on all sides of the tubing and preventing the tube from insulating eachother, if you cant get as many coils as you want build a double structure (frame with in a frame) and you will get more than double what you can fit on the first frame as the second outer frame will have a larger overall diameter.
drill through the side of the fridge file the edges to remove sharpness, use either a rubber gasket or spray foam to insulate the hole after the tubing is through it.
Make sure you leave enough slack inside the fridge coming off the coil so you can pull the entire fram out of the fridge without disturbing the tubes passing in and out of the fridge just in case you ever need to do some thing either to the frame or tubing on it.
I also cant reccomend the pump you would need I havent looked into that at all either. hope this info helps a little.