Irving, where did you find those chips at ? I been looking at amazon but probably much better places that are very specific to these needs ?You'll want an analog output from the accelerometer for sure ( as opposed to digital like I2C to be read by a microcontroller). I would look for the greatest acceleration (g) range possible, as I expect the g level could be fairly high.
An o'scope will give you a time waveform – I'm not sure how much you'll learn from that. An FFT ( which better scopes can do) will shown you the frequencies that make up that waveform.... which may also not tell you much. It would tell you the harmonic frequencies of the barrel, but I suspect this won't tell you much. The natural frequencies (i.e., harmonics) of the barrel are controlled by the geometry and materials of the barrel, but there may be slight shifts in frequency related to pressure in the barrel.
Keep in mind that something long in one domain is sharp in the other. For example, a sine wave continues forever (is broad) in the time domain, but sharp – a single peak –:in the frequency domain. We use this fact to excite natural frequencies of an object. A bump or impact generates broad band vibration that will excite the natural frequencies of the object. An extreme example of this is an anchor drop test on a ship. The anchor and chain are paid out quickly as possible, then snubbed before it reaches the bottom. The resulting impulse will excite the natural frequencies of the hull.
The impulse when the gun is fired will do the same to the barrel, but you'll need to see the frequency domain to make sense of it.