As a rule, is a lower Zener current generally better?
Not always. Zener voltage is affected by its drive current, such that if the drive current is too low the zener voltage will be less than the rated clamp voltage. For instance a 3.3 volt 5 watt zener may need 50 mA to reach its 3.3 volt clamp level. When you are shopping for zener diodes pay close attention to the current they are tested at, usually 50% of the diodes maximum safe current which means it is at 25% to 75% of its maximum wattage rating. For long life diodes and semiconductors in general are seldom driven at more than 50% of their capacity (Be it volts/amps/watts). In your list of 3 zener diodes of which are the same clamp voltage but different bias currents, some numbers really stand out.
BZX79C4V7 = 5 mA Zener current (80 ohms Zener impedance). Notice the low bias current but also the high impedance. It will have less of a grip on the clamp voltage but is OK for low-current general purpose use. With such a low current this is more of a voltage reference, to be boosted by op-amps, etc.
1N5230B = 20 mA (19 ohms). Lower impedance means a more firm grip on the clamp voltage at a somewhat higher bias current. This is a newer product than the last item and one that I would use, though 500mW zeners tend to be voltage references, to be boosted by op-amps, etc.
1N750A = 75 mA (19 ohms). This is an older outdated zener, hence the higher bias current. It will run warmer and waste more current than options 1 or 2. You may see it at a cheap price in bulk quantities from parts brokers but I would avoid it.
The higher wattage zeners are for clamping surges on analog or digital inputs, and for directly driving a low-current load such as CMOS logic or a switching regulator. Often you see 3 watt and 5 watt zener diodes as actual shunt voltage regulators for circuits that need 100mA or less of current. Also the higher wattages go up to several hundred clamp volts, trading volts for milliamps to maintain the 3 to 5 watt limit. Once again, build the circuit to use only 50% or so of the zeners maximum wattage rating.
When possible run the zener at the lowest current where it can maintain its stated clamp voltage, including any loads. Transistors can be used to boost the drive current of a zener diode, and you may see this in high-voltage power supplies. The following stage maybe a switching regulator or CMOS logic running on 15 volts but the source voltage is 170 volts. This is when zener diodes come in handy.