You my friend are a life saver.
I'm going through the exact same thing as the OP. So glad I found this thread. I didn't know the research would negatively effect the score (get me all those -300 warning points).
Love this game, I just couldn't figure out what I was doing wrong.
Researching something doesnt directly give you negative score with the exception of MAGMA deals, given you arent far enough in the mod, MAGMA is a Russian weapons and tech manufacturer and it will trade with XCOM, they generally provide hard hitting weapons that are heavy to carry and use, but hit hard as a truck. As you research advanced tech, MAGMA will send you offers for their exclusive merchandize in offer for alien tech, if you do give them what they want, you instantly get hit by a score penalty and for the rest of the game, random, negative events will pop up from time to time, so its nessesary to pay extra vigiliance and do one extra job to keep the council happy if you happen to get hit by one of these events.
The other thing is, while this is metagaming of the highest degree, but researching new "story arcs" opens up new missions (And negative events) that will start spawning until you resolve the WHOLE arc, opening up...too many cans of worms can lead to you being overwhelmed with missions, this can be both good and bad (Alot of oportunities for good score, experience and loot, but your own sanity and your soldiers life is at risk) but some of the missions and the gear required to completely resolve it are two completely different tech levels.
For example, the Shogg Arc
You initiate it by investigating caves and discover that there is a underground world waiting to get explored, once you get the first research, from top of my head, 3 missions will start spawning, you can get this thing pretty much around promotion 3, by the time, you will be lucky you have the tactical heavy armor for most of your troops (This is an advanced infantry armor that has the bulk required to withstand most firearms without being scratched, once you get this, anti-cult missions will become super easy because only high caliber weapons can even hope to scratch your dudes).
So, you have your metalic armor, blackops weapons and then you start getting these missions
1) Raid
Underground craft spawns in a village with a squad of aliens, armed with
gauss weapons, that will one hit KO your soldiers from frontal hit from full HP unless they roll for ULTRA low damage (The weakest gauss weapon hits for 80 dmg) Gauss Weapons are strongest kinetic weapons in the game and they are meant to be used against things like.... tanks and power armor. Not people.
2) Depthpocalypse
Avoid at any cost, do not, this is mission with difficulty worthy of end game gear, extremely heavily armoured enemies, lots of them and all armed with hard hitting weapons, this is pretty much terror mission by the time you dont even have laser weapons.
3) Croc Assassination
How about the Raid, but instead, you can only take concealed equipment.
There is a silver lining though, the gauss weapons and a new resource type you can get from these missions (esp the raids that are the easier thing here) can be used by humans if you just run these weapons thru research, so if you can bite it down, you can get access to extremely hard hitting weapons relatively early on, you just cant make ammo for it and the raids will be your main source.
And these missions are just the surface of opening this story arc, there is alot more here, but you shall see it for yourself.