There are definitely some combos that are either essential or borderline OP depending on how you look at it. I don’t know if you count mechanics as spoilers, but just in case I’ll insert a break here.
Bethany begins every round with a shield, and one of the ice mechs freezes enemies but also itself. If Bethany has her shield, it negates the freeze on herself, so you can just freeze enemies indefinitely or until you lose the shield. Abe comes with armor, which negates the self damage from lots of different mechs. Camila is immune to smoke which is very useful in the flying mech in Rusting Hulks.
Upgrades are going to depend on your squad and playstyle. Personally I almost never bought secondary weapons unless they were perfectly suited for the squad, like smoke bombs for the Rusting Hulks. I typically would boost my range because all the power in the world doesn’t matter for jack if you can’t get there. After that, each squad usually has one crucial upgrade in it, like chaining damage or not harming allies which I get up front. After that, it’s just a matter of making each unit as powerful as possible and hoping for the best.
Oh, and a tip I didn’t learn until later than I should have. Any ability to generate a shield also applies to buildings.