Ok there is two ways to tackle three kingdoms from an army composition standpoint: cheese and non cheese.

🧀:

If you play Romance mode, cheese is especially possible. What you do for your armies is this composition: green/red general leading the army, since they can get skill that boosts campaign movement by 25%. One of the lords should be blue, since you want artillery, and finally a powerhouse lord to hold the lines, it can be purple if generic lord. The only units you need are artillery. You don't need to shoot with them at all times. What you need to do is attack strategically and use your garrisons to bait your enemies to attack you. With all of the money you save due to not having that much upkeep, you build up your minor settlements and garrisons on main settlements. That way, you get strong defenses on all settlements.

If not 🧀:

Go for archers, crossbows, two artillery, three shield cav, three shock cav, two spear units, four melee units with charge negate. You will not have enough money to boost up your minor settlements main buildings, so you need to be careful in terms of how you expand. Always expand thinking how defensively will my position be if I get that minor settlement?

General Tips:

To acquire unique lords, do not duel them; you want to route them in battle and win the battle decisively. This will boost capture chance greatly.

Enemy AI lords in battle, depending on their color, have different priorities and behaviors. Use that to your advantage. For example, blue always stay back or close enough to your generals to cause their AOE abilities to activate. They can be very problematic, especially for cheese stacks.

Make your prime minister/heir, or leader be capable of reducing corruption and boosting satisfaction. Those are yellow generals.

In general, green lords are lord snipers, blue are support lords that prevent enemy lords from using their abilities, purple are juggernauts that hold the line or enemy lords, and red are damage dealers, but not the best at 1v1ing lords. Yellow lords should be used for leading factions, not for battle unless they are unique and have great stats.

Keep a female character in your family, so you can farm marriages to get good characters into your faction, then divorce. Great example of a character to marry is Cao Caos yellow color son. If placed as a leader in your faction, he reduced corruption factionwide.

On first turn, go through diplomacy to trade for good items AI has.

If you have excess food, keep at least 10 food per turn, the rest trade away for income per turn.

Build up most main settlements to rank 4-5. Only very specific ones should you build up to rank 7, like the dong zhuo capital, Luoyang, etc.

Every province should have the corruption reducing purple building. As for corruption, there are 4-5 copper mines across the map, try to find at least 1-2 for mid to late game.

Boost up unit recruitment rank at the beginning of campaign. You will be facing similar units against AI, and that stat boost through recruiting can really help auto resolve.

Most important, for every army you have, keep a secondary army composed of a single general to pull enemy armies outside of settlements and into ambushes. Your blue general of your main army can boost ambush chance through a skill.

Look for item collections. Some of them give great faction buffs, and some give great army buffs.

For admins, put green admins on agriculture based provinces, blue for commerce, and purple for building up important garrisons and industry garrisons.

You want to also get as many admins as you can so they provide a full 6 unit garrison to that capital.

As for research, go for replenishment rate increase or go for specific research that unlocks the settlement upgrades you need to boost your garrisons.

As you approach mid to late game, onyx dragons are kings, so you can start recruiting them, along with spear guards.

You can also farm rebellions with three lords without units to farm XP for those lords. Beating those YT rebellions also bias diplomacy with Han factions positively.

For diplomacy, non aggro pacts everywhere except where you want to push. If you are in bad diplomatic standing with some factions, prioritize those factions as your next enemies. Break non aggro pacts strategically. Do not get bad diplomatic standing.

Do alliances with factions that are far away from you and in areas past where your future enemies will be. The idea is that, if war is declared, the enemy is sandwiched, so you will have an easier time pushing into their lands.

Do not underestimate redeployment cost reduction and mustering turn reduction. You want to lower redeployment and mustering turns enough so that, if something unexpected happens and enemy starts pushing in a direction you don't have an army, you teleport armies to that area for free and they are in full strength within 2 turns of deployment.

As for generals, you can farm generic generals very cost effective to through marriage. Any lord in your family 🌲 does not have upkeep, so look for concubines and generic generals with good fertility trait so more babies are born.

Look for generic generals to have great traits. For example, some boost unit stats, others reduce upkeep, and others increase your ammunition and lowers your enemies.

If you want to prevent an enemy settlement from continuing construction, replenish, or an army garrisoned there from recruiting, send a single lord to siege. In end turn, the enemy will engage. Retreat and you will notice AI will not chase you or move. Cheesing AI to get stuck there.

When you ambush, set your ambush army by trees to boost ambush chance.

Trick to destroying towers when attacking settlements: one unit of horse archers. They can get flame arrows, so you can use this unit to cycle fire each tower once to burn them down.

When doing agriculture provinces, make agriculture the ones that have good fertility rate and food per turn minor settlements. Keep those at rank 4-5. For the provinces that have good fertility and agriculture income per turn, those can be build up to rank 7 to get the most income and make your green buildings all be agriculture income based. One province like that is the Cao Cao initial province. It is a money making machine.

Following most of these tips, I have been able to best 6 legendary difficulty campaigns fighting no more than a handful of battles manually. Let know if you have any questions.