This is my physics class (all seniors) launching water balloons with slingshots. Due to safety reasons lauchers are hard to find in stores anymore, but I got a decent pair on eBay. None of these videos are great, but the best two are the first two.
If you measure the time that it takes the balloon to travel and the distance it travelled horizontally you can calculate the horizontal speed (s=d/t). Assuming that air resistance is negligible and that the balloon reached the peak of its trajecory at the half-way point (in time) then the maximum height can be calculated using the free-fall formula (d=1/2*g*t^2). From there the average vertical speed can be calculated (s=d/t, using 1/2 of the total time). At this point trigonometry can be used to calculate the angle of launch (and Pythagorean's theorem can be used to calculate the average resultant speed).