This list is in descending order based on importance - which means the GTS (Guerilla Tactics School) and Resistance Ring should be your first two buildings. There are a number of reasons for this that I'll outline below. Assuming you've skipped the "Lost and Found" tutorial to War of the Chosen, the list of buildings you can construct immediately after your first mission is as follows: The first three buildings you choose are potentially the most important factors in how smoothly your early game runs. However, the first two buildings on the avenger will usually be the same in every play through. Personalizing your build order is going to be a large part of developing your system to get what you want out of your early game. You'll often have to play these by your ear and adapt quickly. The final consideration - those random possible that can and will affect your game - will likely be heavily dependent on Dark Events and what strengths or weakenesses your Chosen enemies have. So my priorities would be different than someone who takes a slightly safer or more standardized approach. As a result of this team style, it's quite common for my soldiers to get injured. In WotC, I support these rangers with a Skirmisher, Templar and a support specialist. I like to utilize two rangers and their melee abilities. Personally, I prefer a high risk, high reward style of play for my A team.
But it's worth keeping in mind that the first several structures you work toward will set the tone for your whole campaign. Despite every structure being important, I'm a huge proponent of the idea that you can make nearly any build order work. While I don't believe there is a truly incorrect method in how you start building, there are certainly some strategies that are more useful than others.