Just your everyday fusion-powered ion rocket. Harvest the water/ice, extract the hydrogen through electrolysis, then fuse the hydrogen in your fusion reactor to create copious amounts of energy. The remaining oxygen could be used onboard, or expelled through the ion propulsion system. Use any excess water for cooling (a big problem with nuclear reactors), then expel the steam for additional thrust.
Honestly, you probably have little need to capture additional water for your crew, UNLESS your crew is growing in number during travel. Otherwise, just keep it in a completely separate system from the power system.
Edit: OP updated post to emphasize a desire for complexity. This isn't typically good engineering practice, but can make for good storytelling.
In that case, in addition to the above schema for propulsion and power generation, consider the following "water cycle":
- Harvest water from environment. (If ice, wait for it to melt onboard, cooling the ship.)
- Purify water. Put it in a "cool pure water" tank.
- Separate some of the cool pure water into hydrogen and oxygen, using the hydrogen for fusion as outlined above and the oxygen for ion propulsion, as outlined above. (Oxygen is not the most efficient ion to expel (too light), but if you have an excess, you might as well use it. The helium produced in fusion would be even worse, but could be used similarly. Using these eliminates the need to carry additional ions to expel.)
- Run more of the cool pure water past the nuclear reactor, turning it to steam. (This will also cool the reactor, preventing overheating.)
- Use steam to run turbines, generating electric power. Store the steam temporarily in a "pure steam tank."
- Cool some of the steam into hot pure water in a cooling chamber. (Structure: A strong tank with cool water running in pipes through it. The warmed coolant water will run out to thin fractal panels on the outside of the spaceship, where they will emit black-body radiation into space, thus cooling the coolant again.)
- Further cool any unused hot pure water back into cold pure water, returning it to the "cold pure water".
So now, in addition to electricity and thrust, we have sources of steam, hot pure water, and cool pure water, which any equipment, system, or person on board can tap into. These provide the sources for the hydroponic farms, everyday plumbing, steam hammers, cleaning, etc. When the water gets dirty, it's purified and added back into the cool pure water tank. Of course, these filters will need to be cleaned with water, so there will (unfortunately) always be waste water. The cool waste water should be heated by the ship's cooling system (heat transfer), then to steam by the reactor, and expelled out the back and sides of the ship as high-impulse thrust (very good for turning quickly). This, together with the constant conversion of hydrogen to helium in the reactor, is why the spacecraft must keep harvesting water.
As mentioned above, radiative cooling is a good bet for general cooling. Pump cool pure water through the ship, gathering heat, then through the radiative cooling fins (think metal ferns with water running through the veins). As the fins emit black-body radiation into space, the water will cool again, and heat will leave the ship. If there is excess waste water, additional cooling can be attained by heating it to steam and expelling it for thrust, as mentioned above.