Perhaps there are other strategies, but the satellites/weapons priority works fine for me on Classic Ironman, even in EW. You make up for your shortfall in equipment/abilities on the battlefield with better tactics. Do not be afraid of explosives, they are your friend, especially in the early game. Any loss of weapon fragments is a minor inconvenience if it saves the life of your soldiers. Don't forget that explosives can destroy cover as well. I cannot count the number of times I have used explosives to knock down walls (without damaging anything) just to open up a shot so that another soldier can save one at risk of death. It's not a cake-walk by any means. Even in my successful runs I've taken some big losses, losing some of my best soldiers in months 2-3. However, the game is relatively kind in this regard and if you find yourself running short on a role you'll often see a high ranking soldier of that role pop up as a reward on an abduction mission. If you've gotten panic under control with satellites, you'll have more freedom to select missions like that with rewards you want, instead of having to choose purely based on panic levels.
If the "Matrix-esque guys" you're referring to are the Seekers, there are specific tactics that defend effectively against them. The Seekers uncloak just prior to strangulation, and at that point overwatch gets triggered on them from everyone but the target of the attack. Thus, when you uncover Seekers, everyone at risk of a strangulation attack should try and get within LOS of each other and all be put on overwatch. If you do that, it's very likely that the Seeker will be instantly killed by the overwatch fire when it uncloaks, before it can do any damage. I've also had success by rocketing the area where they went invisible immediately afterwards, though that's something of a gamble.
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