When considering Zener current, is lower current generally better?
The reverse current rating of a Zener diode is somewhat analogous to the forward current rating of a regular diode in that the current rating you would need in a particular application will depend upon the application.

In general, the Zener (reverse breakdown) voltage is dependent on the reverse current actually made to flow thru the Zener in a given application. If you depart very far from the current rating, the Zener voltage will vary from the data sheet rating. Thus, the Zener diode will not be as "precise" in terms of reverse voltage if used at 1/10th the rated reverse current as it will if used at 90% of rated current. You must "fit" the Zener to the application. So, it pays to have as large a variety of voltages and current ratings on-hand as is practical and affordable.

For use as voltage regulators and voltage references Zener diodes have largely been supplanted by IC voltage regulators and IC voltage references because the latter are so inexpensive and small compared to their counterparts of past eras. Still, Zeners have their niche in certain applications. E.g. As spike suppressors in certain inductive load situations.