We hear/feel a pulsating sound/vibration in our house and in our car (when the car is parked at the house. The sound cannot be heard outside. It continues even after the circuit breakers are turned off so we believe the source is external to the house. We would like to measure and characterize it to help us determine the source. There are a plethora of devices out there. How should we select a high quality, but not excessively expensive - if possible - device?
If it is an audible sound, most condenser microphones should record some of it. Since you said hear/feel, I suspect it may be an infrasound (below 20Hz) with harmonics extending to the audio range (>20Hz).
I haven't tried it to be sure, but I think a condenser mic would record the infrasound if you applied enough gain. That's because it is in the nature of filters (the passive HPF that blocks DC from the mic to the mixer/pre-amp, found in all audio devices) to have a slope. If it's a simple passive 1-pole filter (6dB/Oct) set at 20Hz, an infrasound at 10Hz would only need 6dB of amplification to be the same level as a tone at 20Hz.
See if you can rent/borrow the equipment rather than buying it unless you think you might need it for other reasons.