The Throne increases the amount of resources gained from sending out troops. the Barracks increases the amount of actions you have for every turn starting on the next turn after you buy the upgrade. The Mine and Farm give a little passive income of gold and food respectively and decrease the upkeep cost but aren't really worth as much to invest in compared to the Throne and Barracks. So you should focus on upgrading the Throne and Barracks and if you had extra gold after those are maxed you can invest in the Farm and Mine.