I got this "binder" recently. I like it better than any one I've had so far (I'd estimate that I've gone through about eight from various brands).
Pros:
-Very breathable, can exercise in it without feeling like death
-Not terrible in hot weather
-Doesn't show under a lot of shirts, though if you have a shirt with a wide neck it'll show, but does look like an undershirt as opposed to a bra since the neck is high.
-Helps with hiding hip fat
-Feels natural. I forget I'm wearing this sometimes. Probably would be fine sleeping in it as well, though it's good practice to take breaks.
Cons:
-If you have a bigger chest this isn't gonna do the best of jobs binding since it's got less compression than a typical binder. It's still not the worst option in that case, but you won't look completely flat. It's worked well for me flatness wise.
-I wouldn't wear this by itself because it doesn't fit like a regular shirt. Definitely looks an undergarment.
-It smells like a McDonald's playground right out of the package. I recommend you add baking soda into the wash to get the smell out faster.
-I suspect this will stretch out the longer I use it. The solution is to dry it on low as opposed to air dry it. It's got cotton in it so it'll shrink.
I recommend you only get it in black or white if your concern is passing. A lot of cis men will wear undershirts (typically in white, sometimes black, but never in nude).
If you're in-between measurements, order a size up. I made the mistake of getting a size down and I wasn't even able to get it over my head. Had to exchange it which took a while.
If you're interested in a binder with flatter coverage I will post a review of the underworks ultimate binder if requested. Underworks is by far my favorite binder brand for many reasons.
I'm not a Christian but I go to church and have for a while. I recently came out to my church as well. It was a long time coming and I built up to that moment by transitioning in every other way that I could so that it wouldn't be as much of a surprise. My pastor was supportive from the moment that I came out. I sent out a coming out letter to the whole church and got a lot of support. For reference, I live in the rural deep south. My church is a united Methodist church.
I highly recommend that you look around for different churches if this one isn't fitting or you don't feel accepted. Just go to a different one for a Sunday or two and see how the vibe is and how it makes you feel. I have heard that Episcopalians, united Methodists, united church of Christ, and Lutherans are affirming, but a lot of times it will depend on each individual church to what degree.
Another option is to visit a Unitarian Universalist church. Although it is not an explicitly christian church, they are welcoming of Christians and it's kind of a "everyone has their own religious beliefs but we all believe in kindness, helping others, and respect towards each other" deal. They are explicitly affirming and one of the most progressive churches.
Also, if money allows please consider getting couple's therapy with your wife. There are plenty of faith based and non faith based ones out there who can help y'all work through things.