A few years ago we purchased a few sets of these at work:
http://www.rokit.com/uk/ They are really brilliant. I understand you want to make one, I`m sure this could easily be done using their design.
This is the stand they use:

Obviously the fins help hold it straight in flight but more importantly act as a stand. The white plastic you can see is just simply a bottle top and screws onto the neck. The black is a bit of rubber tube. This could easily be made using a bottle top, cutting a hole in it and epoxying a rubber tube in place.
This is the most important part:

One end just screws onto the pump but the other is like a gland and can be hard pushed into the black rubber tubing of the base. When the pressure gets so high, the metal gland is forced out of the black tube, the water is ejected and the rocket fires!
Hope that helps!
Alternatively, you could make this sort of a rocket!