Avenger Optimization (XCOM2)
The Avenger's internal cargo bays can be turned into facilities of various sorts. They are arranged in 4 rows of 3 columns each. The middle bay on the top row starts clear and ready for building; the other 11 will all need to be excavated before they can be used. Excavating requires an adjacent square on the four cardinal directions to be clear, 1 or more Engineers to be assigned to the facility for a time ranging from 5 to 30 days, and will reward you with an amount of Supplies, Alloys, or Elerium Crystals. The deeper you go, the better the rewards, and the longer the excavation time.
Most facilities can only be built once, so despite the lack of adjacency bonuses, placement is still important, particularly with the Workshop.. The only facilities which can be duplicated are Resistance Comms and Power Relays.
The Laboratory provides a place to staff Scientists, and should be an early(top row) construction. It may be upgraded to allow a second scientist to be staffed here. Each scientist staffed here provides an additional boost to research speed. (This is in addition to the boost they provide just for being on the Avenger.)
The laboratory does not synergize with any other facilities.
Advanced Warfare Center
The Advanced Warfare Center provides a dedicated facility for soldiers to receive medical care; soldiers will be automatically assigned here when wounded, and healing speed is improved by 50% when it is available. Additionally, one healthy soldier may be assigned here at a time to retrain their abilities.
One Scientist may be staffed here, increasing the healing rate to a total of 100%.
As you will almost always have wounded soldiers, this facility synergizes well with the Workshop.
In XCOM 2: War of the Chosen, this facility is replaced by the Infirmary and the Training Center.
The Avenger's radio capacity is not limitless, starting at a mere 3 contacts out of a potential 16. Resistance Comms facilities expand this; each Resistance Comms built increases the number of Contacts you can have by 1. Additionally, an Engineer can be staffed here, providing an additional 2 contacts.
The Resistance Comms can be upgraded, which provides one extra point of Contact just for the upgrade, and can staff an extra engineer for an additional 4 contacts(total of 8 with both engineers).
The Resistance Comms synergizes very well with the Workshop.
Guerilla Tactics School
The Guerilla Tactics School allows you to buy various upgrades for your squads, acting similar to the Officer Training School before it. It also allows one healthy Rookie to be assigned here, to be trained into one of the four base classes.
The Guerilla Tactics School does not synergize with any other facility.
The Workshop provides additional hands to do work around the Avenger, in the form of GREMLINs. By assigning an engineer here, you will be given access to two Workshop GREMLINs which can be used as Engineers, but can only staff facilities adjacent to the Workshop. As such, it is thus optimal to build the Workshop in a central location where it is adjacent to many Engineer-staffed facilities. The second row from the top in the Avenger works well for this, and the Workshop synergizes well with Resistance Comms, Power Relays, and the Advanced Warfare Center. Basically, any facility where you would want an engineer staffed full-time should be a candidate for placing next to the Workshop.
The Workshop can be upgraded to provide an additional work slot for an Engineer, who will produce an extra two GREMLINs.
Like previously, all facilities require power to operate. The Research Lab with Tygan provides 12 free power; for any more, you will need to construct Power Relays.
Power Relays provide additional power to run the Avenger's systems. Each Power Relay you build provides 3 power to the Avenger. You may staff an Engineer there to provide an additional 5 power. They may also be upgraded with two different upgrades(which can both be applied). An Elerium Conduit increases the power output by 6(for a total of 10) and an Extra Conduit allows an additional engineer to be staffed there. (+2 passive power, and you can staff a second Engineer for 5 more power.)
Filling a similar role to Steam Vents, the Avenger will have a few randomly placed power coils inside of its building space, usually in the bottom two rows. They will require significant time to shield for use, but once shielded, can be used like any other building spot, with a twist. Any facility placed on a Power Coil uses no power, or if the facility is a power relay, will produce an extra 7 power(for a total of 10). The only facilities on Veteran which cost more than 7 power are the upgraded Shadow Chamber(9 power) and the upgraded Psionics Lab(10 power).
Thus, if you plan on upgrading your Psi Lab so you can train 2 Psi Operatives simultaneously, consider building it on a power coil. The Shadow Chamber upgrade is mandatory, but can be delayed until very late in the game, so it may be more practical to simply assign an Engineer to a Power Relay when it becomes necessary to bring it online. Barring these two options, you should build Power Relays on the Power Coils, and upgrade them as necessary to provide more power.
Replacing the Foundry, the Proving Grounds allows the construction of advanced equipment in a queue. Every project here takes time, and they are worked on in sequence.
An engineer may be staffed here, increasing speed of all projects by 50%. It synergizes with the Workshop.
The Psi Lab provides a space to train a Psi Operative in Psionics. It may be upgraded to allow a second soldier to be trained simultaneously.
The Psi Lab can be staffed by an Engineer, which will increase training speed by 50%. It synergizes with the Workshop.
The Defensive Matrix provides repurposed ADVENT turrets in order to help defend the Avenger in the event of an Avenger defense mission. It at first deploys only two turrets, but can be upgraded to deploy four.
An Engineer may be staffed here, improving the Aim and Damage of the turrets deployed. Note that you cannot enter the Avenger screen once the aliens are preparing for an assault, so you must staff the Engineer ahead of time as 'insurance'. For this reason, it synergizes with the Workshop.
Replacing the Hyperwave Decoder, the Shadow Chamber allows analysis of complex alien artifacts and serves a vital plot purpose; it must be constructed (and later upgraded) in order to complete the game. Like the Hyperwave Decoder, it will reveal the number and type of enemies present in a mission once it is built.
No personnel may be staffed here, so it has little synergy with anything else. It is however the biggest single power drawing room by the time it's fully upgraded, making it a possible candidate for use of a Power Coil space.
Added in War of the Chosen. The Infirmary is where injured soldiers are sent to heal, and can also be used to remove negative traits that cause them to take unwanted actions at inconvenient times. An engineer can be staffed here to double recovery speed. When upgraded, an Elerium Core can be spent to immediately restore a soldier to fighting condition, but this only lasts for a single mission and cannot be used on a given soldier more than once per campaign.
Added in War of the Chosen. This facility allows the spending of Ability Points earned in battle to gain new skills for your soldiers. It is possible to re-spec your soldiers by staffing them here if you wish, but doing so only refunds the soldier's own Ability Points- the ones from the global pool will be lost. Bonded soldiers can also be upgraded to higher bond levels here.
Added in War of the Chosen. This facility is necessary for Covert Actions and Resistance Orders, which will be unlocked as you work with the Resistance Factions. Assigning an Engineer here will reduce the length of Covert Actions.