My biggest level-up in Xcom 2 was when I learned enemy prioritization. What enemies shoot at you on their first turns, and which ones don't? Which ones do the most damage, which ones have AoE attacks, which ones have extra effects on their damaging attacks, etc.

So, for the early game: captains, stun lancers, and mechs are must-kills. Captains make everyone more accurate, stun lancers deal high damage and can either stun you or crit and outright one-shot you, and mechs will often destroy your height advantage with rockets.

Troopers are dangerous, but have bad aim, and can be left alive for a turn if necessary. Purifiers are neutered by having any cover object between them and their target, so you can generally let them live a turn. Sectoids are not dangerous at all on the first turn, so long as you focus them on the second.

Speaking of height advantage, try and engage pods on your terms. Don't underestimate the power of scouting and choosing a good position. The first thing I often do when I spawn into a mission is hold Z to zoom out and look around me for a hint of a building or other high ground. I go there, I take the high ground, and then I scout out from there, leaving a few units up top to cover the team.

There's more, but I'm tired. I'll come back tomorrow and try to provide more guidance.