The opening on the playthrough that worked was proving - awc - power - comms - workshop - psi. Think I built GTS after that. If you aren't buying squad size upgrades, the only good early tactic is vulture which isn't worth an early gts. Sucks having fewer chances at elerium cores, so you need a bit of luck with your grenades and heavy weapons. Aside from vulture, all you really need from the GTS is integrated warfare, the class specific captain traits, and stay with me. Stay With Me seems to lower healing times a little? The increased chance to bleed out instead of die isn't terrible helpful because if you have someone go down when you only have 4, it's probably a failed mission and campaign loss. I rushed PSI that time so that I could get a pair of them cooking up asap, the infinitely reusable lance and rift, assorted extra abilities, and 2 dominations is a big increase in manpower, especially when you score something super tanky like an archon or hit the motherlode with an andromedon or gatekeeper. On legendary, mind controlled archons are basically extended duration mimic beacons, between their larger hp pool, higher defense bonus, and dodge, they soak up an obnoxious amount of fire.
For me the hardest mission in the game by far was the codex coordinates mission. Failed 3 campaigns there, that many chrysallids with only 4 people is really hard and on top of that a guaranteed gatekeeper when you reveal the portal. Failed almost right away rushing it, failed saving it for late, failed once when I was enough of a dumbass to try it with Show of Force active (good god), succeeded when I saved it til after I had two Psi-Ops ready. Setup for the final mission was 2 Psi, 1 Grenadier (mostly gunner specced), 1 Specialist (mostly combat, bit of medic), dominated a Gatekeeper first (to make sure I had two chances to dominate in one round) then an Andromedon for the shredding and acid, two gatekeepers is redundant anyway. Took the mission at a snails pace til I was at the Avatar room, then led the way with a maniple of meat shield psi-zombies to cover my troops. Despite all the cannon fodder my specialist was bleeding out when I killed the third Avatar but she weren't dead yet so I got the no death achievement on top of the rest.
Could load my original veteran/savescum game and drag it out until I've got 2-4 more psi-ops to go for 'who needs Tygan', but that would be pretty tedious, more fun to try it on a separate playthrough.