You should be able to get all the data you you specify with a single MEMS accelerometer for your sensor.
https://www.electro-tech-online.com/custompdfs/2004/01/MMA1220D-1.pdf
is one that Digikey has for 15$. You can measure acceleration directly with this sensor. Velocity is the integral of Acceleration and distance is the integral of Velocity. Vibration will be the high frequency component of the signal.
All of these values can be stored into EEPROM on a microcontroller for readout later.
Brent