Vibration is where mechanical faults show up first, but only if your sensor can see the frequencies where they live. The choice between MEMS and piezoelectric accelerometers is mostly a question of bandwidth and mounting.
What each is good at
MEMS accelerometers are small, cheap, low power and easy to integrate over a digital bus. They are well suited to imbalance, looseness and general running condition, which live at lower frequencies. Piezoelectric sensors extend usable bandwidth considerably higher, which is where early bearing degradation announces itself.
Bandwidth sets what you can detect
Work backwards from the fault. Imbalance and misalignment appear at low multiples of running speed. Bearing defect frequencies sit far higher and depend on the geometry of the bearing. If your sensor and sampling chain roll off below that range, no amount of processing will recover the signal.
Mounting is part of the sensor
The mount is a mechanical filter. A stud or adhesive mount preserves high frequency content. A magnet is convenient and costs you the top of your band. A sensor taped to a painted surface is a low pass filter you did not intend to design. Whatever you choose, keep it identical between installations or your baselines will not be comparable.
Sample rate and aliasing
Sample at least twice your highest frequency of interest, and filter before the converter rather than hoping the signal above that is absent. Aliased energy from a high frequency defect appears as a plausible low frequency feature, which is worse than missing it, because it looks like a real finding.
A practical starting point
For general motor and pump health, a good digital MEMS part with a solid mount covers most of what you need and keeps power and cost low. Add a wideband sensor when bearing prognosis specifically becomes the goal, and be explicit about which faults each channel is expected to catch.