Tl;dr: In a medieval setting, what would be the key steps to gain control (tax, army, police) of a region similar to a city-state?
The region has a central city, with access to the sea, surrounded by few villages in the woods and hills. Its territory is around 3,000 square miles (~7.700 km²). There isn't any local government as the city was recently partially destroyed and its ruling class was wiped out. It is now in the process of being recolonized. In the surrounding area, there isn't a global government, but an alliance of cities. The city of the region was part of this alliance before being partially destroyed.
For the purpose of clarity, consider the region as an Italian city state (like Pisa or Milan, with a Prince, not a republic) that was partially destroyed by a sudden eruption that killed the noble families and ruling class, leaving no legal descendant. What are the key steps someone with lots of money, but otherwise unknown in the political scene, would need to take to take control (tax, army, police) of the unoccupied region? What would be the mistakes to avoid and what would give him an advantage against other ambitious persons having the same idea?
Bonus points for taking in account specifics details of my setting:
No local authority or owner
Growing population of former and new residents. These are people that have abandoned their home after the disaster, but who are trying to come back and new people trying to take advantage of the abandoned buildings
Destroyed local economy, which means that lots of rebuilding needs to be done
But in the end, the main question remains of how to become the ruler of a little city and its surrounding lands, when all you have is money and ambition, but there is no 'land owner' from which you can buy this land.