*Made more edits after a couple of more Deity games after the 9/30 batch.
A lot of these are common knowledge, I just listed ones that I think are important, just to be thorough. This write-up is gear toward a sub 100 Antiquity age finish with war emphasis (1-2 civs wipe) on Immortal+.
Build order:
1. 2-3 scouts first and prioritize on getting gold from huts
2. warehouse building depending on whether you have farms or mines
3. buy 1st settler with 200 gold when hitting pop 5
4. 2nd settler (ideally after settling 3 settlements, with bonus resources and warehouse buildings, you will have the production in capital to build slinger/warrior every 2 turns)
5. 1 warrior+3 slingers build and purchase if you have the gold. goal is to get them asap when you get your first Army commander. Use these 4 units to attack IP units, disperse IPs to get your commander the Initiative and Mobility promotions
6. 3rd settler for 4th city. I usually only settle good city spots with these early settlers that prioritize production and food boost resources like Cotton, Hides, Clay, Gypsum, Wild Game, Wool, Kaolin and good empire resources like silver, gold, Ivory, Marble, and then resources like Camel, Wine, Ruby. Also consider resource clusters for library and barracks, mountain cluster/natural wonders for monument and Villa
7. 1 more warrior, 2-3 more slingers. *the 2 warriors are you meat shields, they build temp fortifications and soak the damages, only use them to attack scouts, commanders, and occasionally city walls, and capture cities. Slingers are your main attackers. The more slingers you have, the faster you can advance and faster commander promotion gains.
8. more warehouse building to boost production/food
9. Library, monument (should have located best spots for these using your warehouse building chains)
10. 2nd army commander to ensure military success, now that the AIs are building more units after the latest patch, this will help a lot
11. 3 More slingers and 1 warrior to fill the 2nd commander, send him to fight along side of the first commander
12. Great Stele and other wonders
Tech:
I generally prioritize production boost tech early, e.g. I might get Masonry before writing if my capital has 3 mines at the time. whatever it takes to get the core army of 6-8 units out asap, even if it means delay of converting 2nd city.
Get Bronze Working after your basic techs to upgrade slingers to archers
IPs:
Befriend a military IP early if possible to get "Age of Heros", it helps the war effort a lot
Another Military IP and Expansion IP for Settlement limit
Science/Culture IPs
General considerations:
1. The earlier you start the war with your neighbor AI the better chance you have to take them down with less effort. Make sure you plan your denounce to allow formal war as you have the army ready
2. protect your slingers, use your 2 warriors in front of them, also use terrains like rough surface, woods to not allow AI melee units to attack them. Use your Army commander's Initiative and Mobility promotions to micro-manage this each turn.
3. Put injured units in the commander, as long as the commander does not move, all units within the commander will heal 10 HP in neutral or 5HP in hostile land on that turn (or 15 and 10 with Field Medic promotion). In your own territory, they will heal 20 in districts, and 15 rural each turn.
4. If AI has walls later, bring 1-2 siege units. Since the game uses Bombard damage against walls, archers have low bombard damage. But once the wall is down, use archers again against unit stationed in the district.
5. If AI has multiple walls up in a city, look around to take down softer targets, or another AI, and come back later once your have stronger commander and siege units. It helps to add some ships to attack if possible.
6. Upgrade to archers (get Bronze working and save some cash) as soon as you can to make fight even easier and faster.
7. It helps a lot if you can settle a town close to your AI target, since you can quickly reinforce your army through unit buying in your forward town.
8. Advance slowly around AI's main city, especially during the start of the war. AI units typically have huge 10+ strength (difficulty level + military aid) advantage over your own units, you might need to use terrain features carefully and concentrate your ranged firepower to kill AI's initial army. And when you don't see many units coming anymore, go attack the town center.
Army commander promotions: (Edited based on Eyswein and MutilationWave's feedback on prioritizing the
Order commendation)
1. Assault-Initiative: most useful for micro-manage attack and heal
2. Maneuver-Mobility: get to the fight faster, also use this to ship your 3rd/4th settlers to a city spot faster especially if there are rough or woods in the way.
3. Assault-Storm: improve slinger damage
4. Assault-Enfilade: path to Order commendation
5. Assault-Advancement + Order commendation: The best commendation greatly enhancing the quality of all your early units.
6. Bastion-Steadfast: improve defense by 2. Your slinger has a low defense of 5, so +2 is huge. Even better never defend with slingers

7. Bastion-Bulwark: Meat shield warriors become even better meat shields
8. Bastion-Defilade: same as above
9. Bastion-Resolute + Merit commendation: love this one, as your guys can heal 5HP after each attack. And Merit lets your super commander command a larger number troops in a larger radius.
*Edit: After these promotions you have a super commander that makes your army fight and defend much more effectively. I moved logistics line out from the first commander since I have seen the return of "carpet of units" from AIs after the latest patch, especially in the exploration age. So focusing on building a pure combat commander becomes more important. I added recommendations for promotions to the 2nd commander below, and he can help to move more troops to the front and assist the first commander in a hot fight while gaining XPs along side.
2nd army commander (for a supportive role initially until gaining the Order commendation) promotions:
1. Assault-Initiative: most useful for micro-manage attack and heal
2. Maneuver-Mobility:
3. Logistics-Quartermaster: path to Regiments, also early gold always helps
4. Logistics-Regiments: carrying more troops to the fight and healing more troops
5. Logistics-Field Medic: use him to heal troops in the front
6. Logistics-Survival Training + Order commendation
7. complete Assault line
Wonders:
1. Great Stele (available early with 2 hammer boost, also early gold helps a lot all around)
2. Gate of all nations
3. Oracle for extra attribute pt. On higher difficulties, if I prioritize production in capital, I can generally built these 3 yielding 600 gold.
4. The Colosseum can be very helpful with the science legacy in the Exploration age as it adds 2 happiness to each quarter, and the Civic gives 1 more settlement limit. Everything else situational.
Let me know if any questions. These are just general ideas that I have learned for ending Ant age early. But I am sure others can add a lot of other ideas.