The above has been presented with a degree of authority, so that comment must be expected.
We could have a debate on the question of which is best, ammeter or voltmeter. However as said, the voltmeter wins hands down on the basis of economy and ease of installation. A center- zero, dual scale ammeter, operating from a shunt at the battery, would most certainly be very useful in all respects and possibly superior. However any technical advantage, hardly warrants the complication involved.
Unfortunately measuring voltage at the lighter socket is not an absolutely accurate indication of battery voltage. Any parallel load on this sub circuit, and there are several, could be dropping the voltage, due to the included line resistance.
If you are fitting a permanent voltmeter, do it properly. Run a voltage sensing wire, via a one amp in-line fuse, close to and connected to the main battery positive terminal. This wire can be of small cross section, as a meter should draw negligible current. Voltage readings will then be independent of any subsequent loads and always reliably accurate. The degree of satisfaction will surely make it worthwhile.
A good idea is to observe battery voltage while the engine is cranking, and with the usual/normal level in mind, one can make a good assessment of battery and or starter condition. Eleven volts or less can be expected.
An interesting worthwhile post for sure.