In my last game I postponed doing the "story missions" for a while. As long as I had enough resources to keep the Avatar Project at a decent level, I just kept doing other things. Building up armor and weapons. I made sure that I had two psi ops that were fully leveled. BTW, the fact that I had to start with a wounded psi op was helped by the training that gave life back for every damage to an enemy. My two sharpshooters were fully handgun trained. Many times fan fire did more damage, after lightning hands, than a single sniper shot. And that allowed them to move more.
In the end I had two blaster bombs and two super shredders. It turned out that psi ops may very well be OP at least at veteran level. Plus the commander's Avatar. Wow. My final group: two gunslinger sharpshooters, two magus psi ops, one bomber grenadier and one almost useless blade ranger. Except for having talon rounds. That helped.
Edit: Last mission? No reason to have anything but WAR armor, even if you never use the bunker ability. Which I never have.