What is the proper dB unit to use when expressing the amplitude of a sample in a digital audio recording?
Your confusion seems to be related to not understanding exactly how decibel measurements work. You say \$20·\log_{10}(amplitude)\$, but this isn't quite correct.

The proper formula is \$20·\log_{10}(\frac{amplitude}{reference})\$, where \$reference\$ is your reference value. The choice of reference value is what determines the full symbol used; if \$reference = 1\mathrm{μV}\$, for example, then the unit would be written as dBμV or dBuV. Likewise, with a millivolt reference, you would write it as dBmV. Current quantities are also written this way, dBμA for example.

Note that the formula is different when dealing with power quantities. With a power measurement, you use \$10·\log_{10}(\frac{amplitude}{reference})\$. The reason 10 is used instead of 20 here is because of the quadratic relationship between power and voltage or power and current.