From your list:
perlite - I use this for cuttings and as a part of basically every “in development” soil mix. The reason being it is the absolute cheapest component that is good at holding air / water.
vermiculite - I’ve tried using this for cuttings but no longer use it for anything
lava rock - I’ve used this for years, but am wondering if its worth it anymore. Its a part of the trifecta of 1:1:1, but I’ve heard some recommend that just pumice / akadama is every bit as good. I will be doing some tests on that someday when I run out of my current stash.
sphugnum moss - air layers and top dressing
sand - I dont have a source for the “sharp sand” mentioned in naka’s books, and regular sand is not generally a good idea for aggregate mixes
akadama - hey it works. I dont use this at all for trees in development, but I do use it for nearly anything in a small pot.
Pumice - This is like perlite that doesn’t get crushed or float. Imo its the best all around soil component for almost anything. Its a bit more expensive than both perlite and DE, so I use a bit of each in development mixes to stretch the pumice out. If I had a cheap source of bulk pumice I might use 100% pumice for quite a lot of trees.
Diatomaceous earth - Ryan did some experiments with this and didnt love it, but I’ve had good luck with using it as one component in mixes of trees in development. This is the next-cheapest component after perlite.
Shredded coconut husk / pine bark - I used to use one or both of these to make my mixes more water retentive and try to make up for the 100 degree summers here. After a few years of testing, I am no longer convinced it actually helps noticeably with water retention or at all.