I'm pretty sure there's a reason that there's different values of hFE for different species of transistors, from power transistors to small signal, and for families of resistors within each species, such as 2n2222 variants and such.
Is the intention to design with specific voltages and currents in mind, and then use the highest gain transistor within a family of transistors that have the general volt/current/frequency behaviors you want?
if you build a circuit for a specific function, do you want the resistors in the circuit to be of much higher values than the internal resistance of the transistor, or do you want the transistor to be of near equal resistance, as long as the volt/current limits are observed? I would imagine the latter makes the circuit more "sensitive" to individual transistors while the former makes the circuit less sensitive. Is that correct?
A maximum stability circuit would allow any gain of transistor, but the gains themselves would be probably pretty low because you'd design the circuit so that it doesn't have a lot of oomph, which would keep the circuit from being unstable given variations in gain across individual transistors (I have managed to build one such circuit in spice), while a more 'efficient' circuit might be designed to push as much gain as possible given a range of gains in a transistor family?
Long story short, what determines your Resistances in your circuits and why you need them of different values all over, and what determines your transistor choice for 2n4401 vs 2n2222 or 2n3904, when they can all work in the same circuit pretty much, given similar voltage and current ratings?