What capacitor types perfom best for large-value signal path applications?
There are actually two cases here, for COUPLING caps specifically, like a mic pre input cap, just make them have really high values so the signal voltage across the cap becomes negligible and so does the distortion, you want the pole way down below the audio band anyway to avoid in band phase shifts (This is not the place to be doing your HPF).  

Timing and filter caps on the other hand are a different problem, for timing my usual instinct if I need more then is convenient with the caps at hand is to stick a little toy micro in there and use that, it is generally cheaper then faffing with tants and multi meg resistors (A toy 8 pin micro with a kB of code space and 64 bytes or ram is cheap, cheap, cheap).! 

That leaves filters, where scaling the resistor values (and eating the noise penalty) is IMHO usually the way to go, then use C0G or film.