The key for a successful career as a lanista is your city and its buildings. There are many different buildings for you to build and upgrade, such as the Gladiator Residence, your HQ or the different Warehouses. In order to advance in the game and to give a proper support for your increasing gladiator roster, you will have to build and upgrade your buildings constantly. Don't neglect your city, or your gladiators' performance will surely suffer!
Every time you build or upgrade one of your buildings, your city as a whole will gain some experience points. Those experience points will help you to raise your overall city level, which will in turn unlock new levels for your HQ. Once you have upgraded your HQ, new upgrades will unlock for the rest of the buildings, and the "cycle" starts anew. All this means that you should always upgrade your HQ when possible, and if you can't, then the best course of action is to make sure every other building is upgraded so you can raise your city level.
Build & upgrade > Raise city level > Upgrade HQ > Unlock new upgrades > Build & upgrade...
Also, keep in mind that your HQ is granting you an "innate" 2.000 capacity for every resource (gold, wood, stone and iron). Sometimes, it may look like you won't have enough storage space for some upgrade, but you will if you take that innate capacity into account.
There are three types of Buildings: