Yup, hate to ruin your day but sound most likely like a head gasket failure. Cylinder 6 is by far the most common, but it could be anywhere. The stuttering is from small amounts of coolant being sucked into the cylinder overnight and being burned off when you start the car the next morning. A mechanic can do a few tests to make sure, but odds are you're screwed (like so many of us with the 4.0).
The sound of water is because you now have a little bit of air in your cooling system, which tends to accumulate around the heater core and can make those "fish bowl" noises in the dash when you start the car, turn sharply, or come to a stop.
Get it fixed, obviously, but you can buy yourself some time if need be: In my '99 Tacoma and my current 4Runner, I've run a radiator/cooling system sealer that bought me some time before repairing. After putting that stuff in the radiator, the problem completely stopped for over 2 years in my Tacoma. And I've got about 3 months of success in my 4Runner so far... Best of luck!