dB measurement
10dB steps are a bit big - the basic unit, the Bel, is rarely used for that reason.
However ...
Assuming you are measuring sound levels, a microphone, amplifier and voltmeter is about what you need to get going. The voltmeter could easily be an LED bargraph
The subject of sound level measurement can be a bit heavy on theory if you worry about the weighting filters that can be used in professional gear -- dBA (common - matches your hearing in normal conditions), dBB, dBC (used for extreme noises - your hearing works differently at a disco!).
Decibels can also be used for comparing voltages, currents, RF aerial efficiency, all sorts of things as it is at its simplest a lograthmic comparison of a known and measured quantity.