I restarted because I wanted to test different early-game strategies and got bored with my save-scumming, and I am replaying with veteran ironman. (So far, I think I could very well have managed everything also with superhuman, because you'll need to abort a lot missions anyway, especially if there are are too many zombies or other monsters for your level of comfort.) I went for both logistics and kevlar vests and then biolabs. I also built a large storage facility early so that I would not need to worry about all the stuff for a long time. But early game research includes a lot of tradeoffs, including how aggressively you try to build up the research capacity versus do research that helps you immediately (e.g. better weapons and transports). A bit further into the game, I'm using humvee and helicopter almost exlusively, and a private car for some missions where these would take too long a time (and a van only in a few undercover missions). I ended up skipping dragonfly, because it seems to be unusable for doing night missions (unless you also use smoke) and you'd really need it only for HQs and other special missions (and it'd take one precious hangar slot). But unless you resort to save/reloads, you likely don't want to go for those missions with 8 units anyway. So I kept harvesting cult safehouses and outposts until I had all the requirements for all cult operations, and researched all of them at the same time at the end of March 1998. So far I have completely skipped exalt liquidation and black lotus party missions as those would likely be lethal. There is already one manor visible on the map and I suppose at least two others invisible (I got chased by cars in Nigeria and Thailand when going on a mission). Now I can get Osprey to go for the missions where completing them safely requires more agents and preferably also supporting units such as dogs and scout drones.
If you play ironman and/or want to avoid save-scumming, you'll need to learn how the sniper/spotter mechanic works. In early missions (apprehension/safehouse) this is not a major factor (though red dawn safehouses also include a few units that can act as snipers), but in later cult missions this is vital. Apparently you can use various grenades and I think also all grenade launchers to take out the cultists so that they don't learn your location and the snipers start targeting you (but if you shoot anyone, the snipers will react and can target you for 2-5 turns depending on their intelligence). You could usually survive their gunfire - so far back they seldom even hit unless they have some sniper rifle - but an occasional grenade, dynamite or grenade launcher shot could wreck you. So, unless you have access to cover that protects you from enemy grenades and/or gunfire, you'll want to avoid firing at the cultists if there are snipers present. With outdoors missions, usually there is no cover, unless you hide below the dragonfly (and then you can no longer leverage the darkness and need to use smoke) or osprey. With cityscape missions, you could go for a nearby building but this is a bit risky as there may be someone inside. One challenge is that occasionally the cult missions spawn in a cityscape environment and sometimes wide-area outdoors and you don't know when equipping the squad which one to prepare for (and all-grenades tactic is risky in cityscape). So for safety, you'll probably need to equip for both and drop the gun if it's an outdoors mission like they typically are.
By always going for the cult missions at night with humvee or helicopter and using mostly grenades and grenade launchers when there are enemy sniper units, the enemy snipers haven't stood a chance and I have also avoided enemy grenades which was an occasional problem when I used sniper rifles from the dark in my previous SH run. The drawback with grenades is that you may end up destroying some of the corpses and the loot (though for example money briefcases and bags are safely stored inside a crate), but better safe than sorry.
By the way, which soldier enhancements are worth it? If I understand correctly, various early-game enhancements usually drop your sanity by some points and I am wondering whether it's worth it in the longer term. But actually, contrary to the text ("permanent cost of 20 Sanity") seems to implicate, they lower the current level, not the maximum, so you can train the lost sanity back up. So a temporary loss of sanity wouldn't actually seem like an issue? This certainly seems to be the case for bio-enhancement (one of my agents is back at the 120 stat cap) and I suppose therefore gun kata is also worth going for. Dagonization does not sound so useful in the paper, but if you can regain the 20 sanity by going on missions, why not? On the other hand, blood boosting harms the bravery and PSI skill as well, so doing that is most likely not a good idea.