What are important inductor parameters to specify for use in a matching circuit?
It's unclear from your circuit if any of the inductors are also carrying a dc current - this can make a significant difference to your choice of inductor size due to saturation properties and the inductance value "retuning" with variable current levels.

Regards the AC side of things, you have hit a couple of important points namely Q and Self-Resonant-Frequency (SRF).

Q is simply a calculation of the inductive reactance at a particular frequency divided by its series equivalent resistive losses. For resistive losses you cannot assume these are measurable at DC - they embrace: -


Skin/proximity effect - as frequency rises more and more of the current hugs the outer periphery of the conductor and doesn't utilize the full cross sectional area of the conductor - it's also called AC resistance. Proximity losses are very related to skin effect - when two wires are closely wound, the electrons flowing at the surface of one wire don't like to be close to the electrons flowing at the surface of the other wire and so they constrict the electron paths through both conductors - it's skin effect plus a bit more!
Core losses which include eddy current losses and hysteresis losses - these both increase at higher frequencies and can be "converted" to some amount of series resistance that adds to DC and skin effect losses.


The bigger Q is at a particular frequency the higher the resonant peak will be in a tuned circuit (not always an advantage of course).

Self resonant frequency is due to the parasitic capacitance of the windings turning an inductive reactance (below SRF) to a capacitve reactance above SRF - if you are using inductors as tuning components then make sure SRF is a lot higher than your maximum operating frequency.

Skin and proximity effects: -