Fortress can be upgrades by repairing successive buildings and rooms. It always cost some money, but increase prestige and security of the stronghold. When upgrading your fortress, you must keep a balance between those two indicators. It will give you high tax level and at the same time you will be protected from too much stealing of goods.
When sleeping in the bed in Brighthollow, you can decide what bonus you want to receive.
During the first phase of the game, you won't have too much money, so you should use it sparingly on further upgrades. Below is a list of few buildings that you should build at first:
Main Keep - It will allow you to welcome visitors and further upgrade the fortress .
Bailey - it cleans up strongholds surroundings and allows further upgrades.
Warden's Lodge - you receive the possibility to get new quests.
Barracks - they allow you to recruit hirelings, and thus increase prestige and safety pretty cheaply.
Dungeons - it allows you to take prisoners during some fights.
Botanical Gardens - each turn your stronghold will produce one random plant that can be taken from the chest in the keep.
You have access to many other buildings from the upgrade menu, but they give you much less profits than the ones above and they should be build in second order. Most of them give you resting bonus. To use it, you must sleep in a bed in the Brightfollow and pick the right option. Bed can be found on the first floor in the room on the left from the stairs. Sadly, available bonuses are much weaker than the ones in inns, so it is better to spend 200 coins and receive better stat boost than to sleep in the stronghold.