Inductors tend to resist any change in current flow. That's why, at the output of the rectifier, besides the parallel mounted filtering capacitor you can use a series inductor (choke) for a better filtering.
Inductance, Not sure what other characteristics there are?
Probably he was referring to their parasitic parallel capacitance and their DC resistance (DCR). Those other characteristics often need to be taken into account. In the case of the OP, probably only the DCR would matter, since you don't want to throw away too much power in the current ripple smoothing function, so you need to use a physically large enough inductor to handle the ripple current without dropping much voltage across the DCR.
Oh yeah, and the inductor has to be physically large enough not to saturate due to the current. So I guess that makes 4 total characteristics of the inductor:
Parallel Capacitance Cp
Saturation Current Isat