Feel free to correct me on anything:
Damage is first run through random chance variable (50%-150% for melee and 0%-200% for ranged), then modified by the armor damage resistance, and then has the armor value subtracted. Anything left over is typically applied as health damage. Damage resistance is typically more beneficial than raw armor values as a result.
Some damage type ignores these rules completely. Lasers are reliable anti-armor as they ignore 1/3 of all armor values and typically no enemy resists them. Chem applies significant damage against armor values *before* they are reduced by said armor values. Bio, charm, smoke and others ignore all armor value.
Melee has reliable damage variables and also most importantly does NOT trigger reaction shots from enemies. Each unit has a melee evasion stat, but this is reduced when flanking from the side and back. Positioning is therefore especially important and your melee gals will use a ton of energy to sprint into position and to swing their weapons. Make sure they have plenty of beer on hand. With proper equipment and positioning, you can one-shot sectopods.
Sometimes faster more fragile armor leads to more survivability than sturdy but slow outfits. You can't get shot at if you're behind cover or otherwise unseen, and you don't need armor if you're not getting shot at.
Capturing people for slavery is almost always the best way to go.
Training your gals happens by doing: accuracy with firing, throwing with grenades which damage enemies, etc. Bravery is reliably trained with seduction and using first aid (alcohol doesn't count) on both injured gals AND bleeding enemies. Bonus of resuscitating downed enemies is another target to shoot at as a way of training firing accuracy. Win-win. You can also seriously game the training algorithm by equipping weapons that have no chance of hurting an otherwise armored enemy (e.g. SMG vs Megapol). See more:
https://www.ufopaedia.org/index.php/ExperienceSeduction trains both Bravery and VooDoo Skill and you can stun out enemies in powered armor reliably in 1-3 hits. The downside is the Seductress outfit is very fragile. Keep a canteen on hand to reduce stun damage.
Research is not as important as in vanilla XCOM, especially with how expensive brainers are. More paramount is ensuring you have a steady and reliable source of income and that is based on selling loot and manufacturing merchandise. You should invest most of your money into expanding your manufacturing capacity early on.
You can safely sell any chips you loot as counterfeiting is not necessarily game-breakingly profitable and comes rather late in the game. Chateau distilling is an early game item that remains profitable for a long time and Apples are the primary reason to go after all missions happening in villages (typically LokNar assistance, but sometimes UFO crash landings). Apples also allow you to make Rum which is an extremely useful and versatile item you'll use into the late game so don't spend it all on Chateau.
Keep all integrated devices, optronic components, and force circuitry no matter how tempting their selling price might be. They're useful components in higher level manufacturing.
Crackdowns are faction specific so don't go after enemies you don't want to take on inside your base. This primarily means staying far away from Mercenaries and Star Gods shipping. Mercs are heavily armored and have sky-high reactions; while Star Gods are shielded, have dangerous Psi capabilities, and come with Sectopods.
There is a surrender mechanic which depends on the remaining morale of the enemy units. If you find that it hasn't triggered yet, it most likely is being held up by an enemy which doesn't or rarely panics (e.g. academy drones or attack dogs).
Enabling debug mode can help overcome some of the tedium present. Ctrl+D reveals the entire map, Ctrl+W teleports units to where you click, Ctrl+J stuns everyone, Ctrl+K kills everyone. This can significantly save time on missions which have an obvious outcome. Debug mode also acts as a great experimental lab for you to test out different weapons.
SMGs are typically not that great for your gals as their primary benefit (low-weight) only helps slaves and peasant soldiers. Exceptions apply to one-handed SMGs like Death Blossom which are a perfect side-arm for melee gals. Rifles with auto-shot capabilities are an excellent choice for standard issue equipment. Rifles have infinite range for aimed shots, this means that as long as you can spot the target, there is no drop-off by distance. Pistols are good for melee gals and infiltration missions.
Dropping explosives is 100% accurate and uses significantly less TUs than throwing (~4 vs. 30).
Dogs are near-perfect base defense units. Very fast, built-in Aye Phone, and their bite *could* potentially damage powered armor units with a lucky roll.
Some health damage helps reduce the chance that enemies will regenerate stun. Alternatively, smoke grenades are a reliable way of ensuring that stunned enemies stay down because they apply stun damage every turn so long as the enemy isn't choking immune.