Are there any details on what advancing the plot of the game does? I’ve stalled by not researching the church data bank, but I finally bagged a navigator so I’m planning to start pushing that research.
First run where I’ve made exposuits too, and I have to say I love these things
You can see "Affects game progression" in the tech tree viewer on the critical ones (one can also search for research prerequisites in ruleset files; this is the only way you can find out how those techs actually affect game progression).
"Church" research branch essentially only gives you access to barracudas (and dependent techs). Going down that tree stops church missions except the attacks on military installation (goodbye easy missions). But getting barracuda as early as possible, to be able to shoot down subs and protect the transports, is crucial. So you'll need to obtain an alien corpse and research it ASAP, to get started on alien containment. The easiest way to capture live aliens after that are stun grenades on land-based missions. In early game, I've also always obtained harpoons with SC ammo and stun ammo, to be able stun aquatoids if an underwater medium/large sub comes up before obtaining a navigator through some other means.
Several other interconnected branches give more for example weaponry (navigator, high navigator, high engineer, bio-drone terrorist being most crucial; you'll also need a freak leader later). You'll also need MC reader, and examination room from a very large ship is also essential to get anywhere. You'll need to build a couple of biolabs and MC labs in your most essential bases as early as possible.
An aquatoid navigator is rather straightforward to catch (you'll need to be prepared to stun almost every aquatoid in a medium ship and kill the rest). Bio-drones are most easily dealt with with a huge number of stun grenades (or if you get close by, with a tazer). In my RNG, I've always got lobsterman technician before armored gillman engineer; you see lobster technicians on small ships. At this point you might not have sonic yet and obtaining a live one (let alone killing the rest) is very challenging, depending on the landscape. Jellymen weaponry (squeezer to kill lobsters, tangler to capture them) is essentially a requirement. If you have these, I've usually managed a capture without many casualties. How you end up obtaining high navigator (usually enhanced aquatoid) depends a lot on RNG. A terror mission is likely the easiest, but this branch might be significantly delayed (until you have MC protection, i.e. when you can finish the alien lab or barge)
For the main game, you'll need to learn more of nagas, get a naga lord so that you can get to naga city. You'll need to go through the alien dungeon (no sense even trying the second part prior to sonic tech). You'll need a lobsterman commander as per vanilla. You'll need to learn of the jellymen and go through a jellymen base to get the treaty with the jellymen (capturing a jellyman ruler from the base is enough; I'm not sure if you get the treaty regardless if you clear the base and kill everyone).
There are some more minor things to note (e.g. getting thermal tazer, getting live and dead deep one, etc.), but those should be easy to discover and figure out.