I typically start with the zones pertinent to the character I'm starting to read them on - so for my mains that would be Daggerfall Covenant, reading them in game order from Stros M'kai through Rivenspire and following on with added DLC content. Then before I read everything else non-germane to DC on those characters, I'll pick up a character on AD, and then one on EP, and read those zones.
After that, I'll read DLC zones, and anything I have from the group content areas and Cyrodiil/IC (not that much as I don't do group content or pvp).
I generally don't read for "lore reasons" on every alt - I have a ton of alts, and after reading the faction zone books on mains, I tend to just get what I have to have for mages guild on alts I need that for (which isn't all of them for sure).