peltier is the easiest way to go, and the least efficient
you need a "water block", which is a heat exchanger... energy from the water is extracted by a copper or aluminum block that has channels inside it. the peltier heatpump then removes the heat energy from the block.
check out some auction sites for a used peltier waterblock CPU cooler, wash it out really good, and plumb it into your water supply ... then just hook up a beefy power supply to the peltier, either with microprocessor control or a simple comparator and thermal probe.
The systems I've seen use a small 0.5 gal (or less) reservoir to store the chilled water, constantly circuilating it through the water block... since just one pass isn't going to remove much heat.
The peltier will also heat your water for you, just reverse the polarity and the cold side now gets very hot - use an H-bridge and you can do both with one setup.