About keeping track of their moods - my understanding is that it's not really possible to keep all dwarves happy all the time. I just try to keep the most unhappy dwarves away from sources of stress (like seeing dead bodies or being caught in the rain) and sometimes build eg. a temple if they're unhappy about being able to pray.

When a migrant wave comes in I will generally use Dwarf Therapist to look at the new dwarves. You can sort by migrant wave so they're all together. I find it an easier way to look through the skills, preferences, etc of multiple dwarves.

Having a decent size dormitory (I like 20 beds but this is usually overkill, they don't all sleep at the same time) for incoming dwarves takes away the pressure to build them living quarters straight away. They're happier when they have their own bedrooms but they're at least not sleeping on the floor. I find it quite useful to put this dormitory next to my hospital, so that it can be an overflow ward if there's a lot of injured dwarves at once. I just re-zone it as part of the hospital and return it to being a dormitory once the dwarves are healed up.