Choose Zhao Ming and The Western Provinces
Zhao Ming is a Grand Cathay Legendary Lord included with Total War: Warhammer III. The new-player guide names him as an approachable Cathayan start: a dragon lord with a combined-arms army. Select Grand Cathay and The Western Provinces in Immortal Empires. He can also lead a Realm of Chaos campaign, so match the mode before you follow a map plan.
His west is tied to Shang-Yang and its alchemists. Miao Ying's Northern Provinces are the Great Bastion campaign on the same race. Learn one of those openings before you treat every Cathayan dragon as the same map.
Keep the west supplied
Inspect the starting province, the wars already open and the route back to your settlements before the first march. A caravan on the Ivory Road is a separate trip from the army that holds the home province. Patch 5.2 lets Zhao Ming dispatch two caravans from the start, and a technology available to Cathayan factions can add another slot. Send a caravan when the field army can still answer a threat at home.
After you take a settlement, check what the new border asks that army to defend. Distant trade does not hold a province by itself.
Harmony, the compass and research
Battle Harmony is the relationship between Yin and Yang troops. Update 8.0's Harmonic Anchoring skill lets an Alchemist count as both for that pairing. Position the regiments that should support each other, and keep a regiment for the flank instead of sending every unit off alone.
The Wu Xing Compass is Cathay's other shared campaign tool beside the Ivory Road. Use it on the same turn you spend on settlements and the field army. Update 8.0 split Cathayan technology into a Military tree and a Provinces tree. Military research improves units and fighting. Provinces research covers settlement management, the economy and actions on the campaign map. Pick the tree that matches the problem in front of you.
A line in front of the rockets
Jade Warriors hold the centre. Missiles and the Fire Rain Rocket Battery need a lane and time. Zhao Ming fights as a human spellcaster or as a dragon. The dragon is a large body for a gap in that line. It is a poor substitute for the infantry standing in front of the rockets.
An Alchemist adds Metal magic. An Astromancer adds Heavens. Either hero joins an army you already have. Read the spell, cast it into a fight you can see, and keep the hero out of the rocket's landing area.
Other Cathay campaigns are separate purchases
Miao Ying is the other Warhammer III dragon, on the Great Bastion. Yuan Bo comes with Shadows of Change and leads The Jade Court. Bhashiva is a character pack: the Claws of the White Tiger, with the Tiger Court and Iron Favour. Saytang the Watcher is a Legendary Hero from Shadows of Change. He joins an army through his recruitment chain.
Learn Zhao Ming's line, caravans and research before you buy another Cathayan lord for a different system.
Recover, then choose the next commitment
Check casualties, any caravan still on the road and the nearest enemy after a battle. Replace the role you lost: a holding regiment, a missile lane or the artillery. Open another front when the west can spare the army.
Katarin and Karl Franz are the other base-game lessons in a supported line. Thorgrim, Tyrion and Mannfred are the openings once you own the first or second game.