I know they have the data somewhere to see what dungeons are continually popular, but I'd honestly just lump all the dungeons together into a single giant pile and go random from there.

If there is a need to split it, I'd say have a single roulette for the last expansion or two. (so 61+ or 71+ currently) and another for "Everything else".

Ideally it'd keep wait times down on the most current content, but who knows.

Also, I'd say rename the trials to make sense of it:
Trials in story mode (the early 4 mans) get called that (so "Bowl of Embers: Story Mode")
Subsequent Trials drop the silly "Extreme" or "Savage" and just get stars (so HM is 1 star, EX is 2, if they decide to add more like Savage, go 3 stars and so on)

Each language has a different goofy name for the different tiers of trial which don't make sense. And there isn't even a normal mode for many trials which is, again, goofy.

...ideally I'd love this easy "star" system to also be applied to dungeons, since it opens up the possibility of having a 3rd run in certain dungeons..assuming they ever decide they want more than 1 dungeon per major patch. Would be easy to recycle older "tilesets".