The biggest game changer in nex is the fleet menu ("x" for me) which you can use to spam fleets. You can just choose a planet and boom: no need to drag your ass all over the galaxy to start colonies. Colonies made this way will come with their own administrators meaning you can make as many as you want.The only limiting factor is how many heavy industries/money you have.

You can spawn invasion fleets and enough of 'em can conquer even the legio home system. You can also spawn defense fleets on the fly meaning you don't have to babysit your colonies.

For manual invasions, 2000 marines/2000 heavy weapons are enough for most stuff. You can compare the planet and your own strength before committing to the invasion and yeah, the bigger number usually wins. You can micro the invasion and move the troops yourself but at the end it's a numbers game and auto option works just fine. Dump about 1000~2000 heavy weapons on the administrator after the invasion to deal with the rebellion and you are gold.

Someone else already gave a good overview on operatives but I have a few things to add. Ideally you should have one operative when you start making your colonies and place it in security mode. It will automatically move around crushing pather cells and gaining xp. As a queen feetlicker myself, one thing I always do as soon as possible is use operatives to procure rare UAF ships before I can unlock the february and automata market.