(0) You should be trying to run ONE SQUAD containing one of each class. The anti-tired perk is absolutely, utterly king, followed by the removal of any serious trait needing redemption, followed by accuracy and crit, followed by health (not armour, because lategame you'll 100% definitely be shot naked, meaning that armour is strictly win-more, not swing-to-win), followed by resourcefulness (ammo from rests), followed by team spirit (more command points), followed by reload speed (which is really just a crutch for not managing your marines well enough, but definitely reduces fubar encounter rates when dicey things occur).
Upgrade-wise, silenced sniper, full sergeant comms pack, full accuracy/suppression smartgun (don't bother with the tripod), full medic set, no techer drone.
Beyond the class upgrades, the generic picks should be accuracy, then wide magazines, then extra tools/ammo.
Always take the smartgun, and always run one pulse rifle. Its grenade launcher will make so many set-piece encounters more efficient, especially vs the ranged enemies. Always run at least one heavy pulse, as the ROF combos with the plasma rifles to chip off low-hp, already-plasma-chunked targets.
During missions, look after the squad's stress as much as their health. Do the entire mission in one run and heal them up. It's strictly optimal to take more days healing the same elite unit then spreading XP over mediocre fodder and making multiple trips to the same site.
On ironman + nightmare mode I was able to run the same 4+ guys every single time (and if you're not managing these so-called XCOM bits well enough to achieve this, you are probably going to be seriously underpowered for the tougher missions (on nightmare) to the point where I doubt they are possible without intense - seriously intense - failure streaks). The atmosphere processor (mission 6ish?) and the Darwin Era ship (mission 8ish?) on nightmare without some level ~10 guys?... very very rough.

(1) During missions, when you are presented with an actual challenge at whatever point, however subjectively, whatever the context, the prime solution is about STEALTH. Maximise THAT.
Silenced sniping; mines; sentries; AFV; motion trackers. Keep the detection meter from moving. Keep stress from building. Plan ahead for the unavoidable onslaughts and such due to the hunt timer acceleration once you do actually get spotted (see 3).

(2) When that's not an option, maximise MISDIRECTION.
Reshuffle what the enemies are doing and how they are pathing. Notice how many spawn rates/locations and paths change when you walk your team into new areas or open a door for the first time. Use motion tracker overloads. Create areas of denial as the enemies often stop pathing to areas flooded with mines/sentries in costly positions to attack. Bait their movements with overloads/techer drone (though the serious glitches with the techer drone meant that I didn't take that upgrade on my second run in nightmare mode - it's a total liability).

(3) Fight in PLANNED KILLZONES to your advantage.
Avoid running and gunning where possible. If a fight starts, return to a sentry/mine/AFV-controlled area, or at least to an area that has enemy ingress paths covered by such.
Deploy sentries readily. Resupply them at 100 or so. Always be carrying a full set; bring them with you once the killzone has served its purpose.
Use the flamer to (primarily) further control the enemy pathing, with damage being a bonus.
Spam the anti-stress ability from the Serg.
The shotgun rescues the fights that are going wrong.
Keep moving around where possible, force the enemies to proc their less-direct attacks/moves, buying more dps time.
Scream "Let's rock!" IRL and get the job done, marine.