To be honest it doesn't really matter which type you use and pf value caps tend to only be available in ceramic or multi layer ceramic types. My preference for everything else is poly box caps up to 1uf and I tend to use electrolytic caps for everything higher but only because I bought a job lot of them a while back.
Will switching between the same values in different types (i.e between ceramic disc, multi-layer and poly box) give a noticeable difference in the sound, or would it be too insignificant to be able to tell?
Subtle at best, but it's something you need to answer yourself because everyone is different with that. The difference would be considerably more obvious if you changed the cap value and so I really don't think the type is anything to worry about. I use polyester or multilayer ceramic up to 1u, and then electrolytics or tantalums depending on whether I'm stuck for space. They all make great sounding effects.