That last part is why I'm thinking a peak detector wouldn't be quite right. In addition to the peak, you would want to see the total area under the curve.
I actually have one of those red MSI sensors. I just hooked it up and smacked it around a little. Barely got more than a volt, and that's with no padding. "Lots of voltage" may mean something very different than you think - that's a HUGE voltage for a sensor, but not so much for damaging things.
The duration of the pulse was in the millisecond range, and it's AC.
If you have one side hooked to the positive supply and the other to analog ground, you're doing it wrong. Connect one side to analog ground and the other to the analog input pin. No positive supply at all. See how that reads.
What is the fastest samples/second on your Velleman? It ought to read in the khz range.
I think the peak would correspond to impact speed, and the area under the curve is going to give an indication of the total energy delivered by the blow.
Calibrate it by swinging a known weight on a rope from a known height, maybe.