fletching/bodkin/bracer are the absolute most important and should be picked up immediately
after those i would prioritise husbandry next if my enemy is making melee units or bloodlines if they’re making ranged units.
you want both fairly soon anyway
against melee units armour upgrades can be delayed a lot but they’re more important against ranged units
ballistics is very important if you want to raid but can often be delayed otherwise
thumb ring is much more important for CA than mangudai (which already have high base accuracy and fire rate) and i wouldn’t get it for mangudai until on the way to imp at the earliest.
for CA you might delay it until then as well if you’re doing more raiding than taking direct fights
parthian tactics is relatively cheap and good to get early imp, especially if your opponent is going for halbs.
maybe delay it if they’re not making halb
chemistry should be picked up ASAP in imp
usually the last thing you get (except maybe an armour upgrade or two) will be heavy CA/elite mangudai, simply because these are very expensive upgrades