Choose Mannfred and The Drakenhof Conclave
Mannfred von Carstein leads The Drakenhof Conclave. Total War: Warhammer, the first game, unlocks him and Heinrich Kemmler in Immortal Empires. Keep that purchase on the same storefront. He uses the Lores of Vampires and Death and can fight in melee. Decide whether the next order is a spell or a swing. A lord stuck in a duel cannot support the line.
His campaign follows the Books of Nagash. Open that panel before you march toward a book the army cannot protect on the way home.
Keep a province you can raise from
Look at the borders, the armies already in range and the settlements that will feed recruitment. An undead line still needs a province you can return to. Taking ground and walking away leaves the next fight without a place to raise replacements.
Raise Dead, Corpses and Blood
The Lords of the End Times free-content article makes Raise Dead the default way Vampire Counts recruit. With the capacity and the resource, a regiment can be raised away from the province that built the military chain. Military buildings raise that capacity. Recruitment no longer depends on a chance roll at a battle marker.
Corpses are a provincial resource. Units killed in the province add to it, and larger battles leave more. Lower-tier regiments recruit with Corpses. Higher-tier regiments also spend Blood. Buildings in the province can turn Corpses into Blood. Blood is also spent on Vampire Lairs, Bloodlines, confederation, some buildings and technologies. Spend it on the next march, not on every option at once.
A Vampire Lair, once you have discovered the settlement that hides it, is developed before the vampire inside wakes as a lord. A short awakening and a long one are different investments. Bloodlines are empowered from that same Blood pool, and later empowerments ask for more.
A line that pins, and a lord who chooses
Skeleton Warriors establish the line. Grave Guard go to the part of the fight that needs more than a pinning regiment. Mannfred casts or steps in where that line needs him, and he keeps a way back out when missiles or an enemy character turn on him.
The skeletons hold. Cavalry, a monster or the lord supplies the blow around that pin. Give each of those a target the skeletons are already occupying.
Other Vampire Counts campaigns
Kemmler also comes with the first game and leads The Barrow Legion. SEGA lists Vlad von Carstein and Isabella von Carstein with the first game and with The Grim and the Grave. Free content for the race follows ownership of the race. Helman Ghorst is The Grim and the Grave. The new-player guide says purchasing Nagash also unlocks Neferata. She is a separate Vampire Counts campaign.
Dieter Helsnicht and Walach Harkon are Legendary Heroes from the Nagash content. They can join a Vampire Counts faction when that content is owned. Ulrika's route into Neferata's faction is a technology, different from her mission chain for Kislev or the Empire.
Count the dead, then spend Blood
After a battle, check casualties, the Corpses in the province where you fought and the Blood you might rather save for a lair or a higher-tier regiment. Replace the skeletons that held the line before you chase a Book across the map.
Zhao Ming, Thorgrim and Tyrion are the other first campaigns for Cathay, the Dwarfs and the High Elves. Karl Franz is the first game's other lesson, on the Empire side of the same map.