Thanks for the tips guys, I honestly can't see how I'd make it through this game without cheating. I had a couple of easy missions and then bam, my ship got hit by a roaming UFO and it had the makings for a total bloodbath.
In general while I like how it plays out thematically, it definitely feels like the player is operating at a huge deficit. I guess that's part of the appeal of this game, but it seems so far unbalanced when the enemy has so many advantages over you (tech, numbers, psionics, resurrection, teleportation).
Anyway, just curious approx. how many missions (I know it depends on how you play) did you play before you reach the "finale"? I'm guessing it's made clear when you are at the finale?
What I have been doing is countering what I consider the worst enemy effects. Blocking attacks on the UFO seemed #1 because I haven't built any ship defenses. If not those I'll block things that can make missions a pain, like poison rounds.
Also, take your time and build up your tech. You can quickly knock down the doom counter by doing story missions, so don't freak out if it starts getting high. If you can, choose missions that are "difficult" or lower because you should be able to get out of them in reasonably good shape. Also, try to keep reasonably stocked with rookies you can bring on if necessary. They are cheap, and the alternative is getting caught understaffed.
Edit: oh and by the way there is a point in the game where you will get the ability to see what enemies are in each mission. Use that to your advantage when setting up your loadouts. If you are going up against robots, for example, bring bluescreen rounds, emp grenades, a specialist with combat specialization, etc. and you will clean up.
I'm sure more experienced players can play through in a much more streamlined manner, but if you are learning like me, taking your time is your key to success.