I just play with whatever I've got at the time - if there is a card in my hand that can be immediately useful (even if not very), I'll most likely play it, picking the option that seems the most useful if more than one card could be played. Especially if it's someone like the Adept where I know I'm gonna want as many songs and instruments out as possible since I never know what I'm gonna end up with in subsequent turns. If my hand only consists of instruments, I'll play to set up for the "power combo" if either or both of those instruments is the Harp/Lyra, otherwise play any other one. If my hand only consists of songs and it's still the first turn (so I have nothing already in play that I can combo with) then I'll just play whatever will be most useful this turn unless I have Inspiring Supertonic in which case that's going out ;).
Anyway, speaking more generally, I never play based on "Oh, I just need to wait for this one card and then I can do these things". It's more a case of "If I can get hold of this card I can do all these things, but in the meantime I don't so I'll just do this other thing instead". And sometimes I'll have a card that could be at least slightly useful now, but I'd prefer to hold onto it later so I can take advangate of everything it can do, for example if I have a copy of Disruptive Flechettes in-hand when the villain has no horrible ongoings in play but I know they could do (eg Return with the Dawn, Apocalypse) so I'd rather hold onto it in case they suddenly play it. Unless someone else has ongoing destruction too, in which case I'd probably play it if there were a whole bunch of targets to hit and thus take most advantage of the damage. Or if it's someone like the Ennead who have no ongongs at all, in which case Flechettes becomes solely a damage card.