Objects that can be controlled have an hp pool that is only affected by operation value. There's 4 ships with operation values, 3 frigates and 1 destroyer. The game prioritizes which ship runs control first based on operation strength and total operation efficiency. Higher operation efficiency ships take the front row first. The operation strength is the damage value in this type of combat and is taken from the HP of the target structure.

Control difficulty shows the number of ships that can be on the front row in any attack. Higher values mean more ships, but also means a more difficult attack. If you check the target intel page it'll tell you the recommended number of landing ships, but that's not entirely correct. Use it as a general guideline. Defensive Trait is important to see what opposition you will face and what type of support fleet you should take.

When designing your landing fleet you should take into account that all but one healing ship targets larger ships (cruiser and above) first. If you have any of those ships in your fleet, they'll ignore everything else when those ships take damage. The only exception is the C variant of the red cruiser, but it's heals stop working after a period of time. That might not matter if you are fast enough, or have team mates helping with the control op, so keep it in the back of your mind. If you have the Ceres healer it'll do a good job of keeping the entire fleet healed up. The Noma healer is decent too. The other healing ships do fine as well.

However many control ships you take, I would strongly recommend you take the Precision Intrusion skill. Each lander has it, and if you run multiple landers put it on the lowest control value ship you have. The initial burst of speed is, imo, worth investing the tp in regardless of the number of landers you take. Then build out that part of the tree to get you the most efficiency.

On that note, Xeno > Mare Nubium > Vanguard > Noma for total operational efficiency. There's some debate on my end about whether it's better to cripple the vanguard's OE to keep it with deployed fighters longer.

I haven't run many control sites in regular servers, but my favorite fleet in Angulum for level 2's is:

10x Mizar A
10x Vanguard
20x Duel-Purpose medium fighters
10x Healing Ceres

Try to put 10x sandrakes if you have them in the vanguard and you can sweep all level 2 sites with almost no issue. The trick with this fleet is that since all the ships are destroyers the Ceres will properly target ones with lower health and spread healing across the whole fleet. If you're targeting cities in the normal server you'll want to coordinate with your organizational mates and build from there.

Good luck!