It depends on what you want to know!
Obviously, you will be billed for power while you are an ordinary household, but if you are a large consumer, because a poor power factor costs your electricity supplier more - both in losses but also because bigger cables and larger transformers are needed - it is likely that you will also be penalised if your power factor falls too far.
Generally, the power supply system is inductive, so if you have a large load with a low and capacitive power factor, it will tend to cause the voltage to rise, which could reduce the life of your appliances if it rises too far. In that case, voltage is quite interesting.
If your concern is cable ratings and circuit breaker or fuse ratings, then current is most important.
I don’t know if it applies where you are, but in the UK, I can log voltage and frequency, and watch how generating capacity is added and removed as the system load changes during the day.