One - ugh on the merge... politics of such can get messy. Good Luck
And, I'm in an environment with too many of our denomination churches for current (and declining) attendance. So as much as folks don't want to hear it, a 'merger' is likely in our future as well. But to your question
So for my church, I set up our livestream environment with the start of COVID.
What you don't mention above, but factored into my purchase decision, was expected life and use of the system
- In my case, I expect a PC to last at least 4 years (preferably 5) and though we were streaming last year at 720p, wea are streaming 1080p now (and have been recording 1080p since early on). Ideally, I wanted a system that could stream at 4K, should that become mainstream in the years to come. But I realize that may be fanciful thinking, at best.
- Further, I expected that occasionally, some of the service content (recorded locally for higher bitrate/quality) would be desired for other reasons, be that to share with family for baptism, wedding, or funeral, or a small snippet for marketing purposes, etc. As such, with all the other church PCs be older and under-powered for video editing, the OBS PC would be capable of video editing as well.
Recognizing that real-time video encoding is VERY computationally demanding, my initial interest was in a NUC (with 6c/12t being my minimum consideration, and 8c/16t being desired and I ended up with an i7-10700K at the time [I'd have preferred Ryzen but close enough])
I started with an engineering class (Dell Precision) laptop workstation. And it ran our setup fine. However, I needed to switch to church PC, so checked into using a donated circa 2015 gaming laptop with an i5-6300HQ (4c/4t), 8GB RAM, Nvidia GeForce GTX 960M, SATA SSD with a fresh optimized Win 10 Home edition, and failed (and not due to RAM)... Now, in what I've learned since, I could have probably gotten it to work, eventually. But my focus was on service delivery, not OBS optimization, so we decided to buy a PC. I really wanted a NUC, but a key considerations is getting nVidia's Turing based or newer NVENC for video encode offload to GPU. That means a GTX 1650 Super or better. And I could find a NUC with a current gen CPU and that GPU, with adequate support, so I got a new business class tower PC with next business day onsite support.
And laptops will almost always thermal throttle long before a desktop. Can you do this with a decent laptop? sure. but i'd still pick a NUC over a laptop for this use case.
I mention all of this only as food for thought.
When I was using the laptop, I quickly needed to add a 2nd monitor, so really a laptop vs small tower really doesn't make that much difference (though I admit I'm not moving my setup now that we are back in person and got a PTZ camera).
So, without knowing budget, longevity, etc, and assuming better value to pay a little more now and get 2X the life, I'd still spec a similar system as I got. For CPU vulnerability reasons, I'd prefer to avoid 11th gen Intel CPUs and earlier. [yes, I ended up with 10th gen.. so its not a hard rule of mine, just a strong preference for 12th gen intel, or recent Ryzen]. And, you could do all the encoding in CPU, so if PC building is something you are, or have easy access to, it may make sense to get a current good CPU with GPU built-in, and know CPU usage will be higher now, but late in 2022 or whenever GPU prices come back down to earth, to get a decent NVENC capable GPU [I won't repeat why not to target an AMD GPU for use with OBS, plenty of other threads on that subject].
As for the rest
- beware USB Root Hub limitations, when dealing with 2x 1080 video streams on input. Cheap chipsets sometimes choke. If you get something with multiple 10Gbps USB ports, hopefully you'll be okay
- video is important, but audio even more so. Do these churches have an in-Sanctuary sound systems already? if yes, I'd want to take that audio, adjust for livestreaming, and use that (I currently use an analog cable from mixer, using a sub-mix, though a gain adapter, into PC. It took some fiddling to get audio levels correct, but works nicely.) One thing to be aware of is that certain audio sources (pipe organ, piano, choir, etc) may not need amplification for in-person attendees, but should be mic'ed for remote listeners.
And then there is the loss of audio directionality and typical poor speakers for remote users, so Audio Compression often helps (as well as other more advanced Audio filters and effects). but really depends on worship style, audio content (spoken vs varying music types, et) as to what is needed for a decent remote participation experience
another consideration is camera control (and possibly audio mixer) and number of volunteers. For me, we have a set once and not touch type audio setup. So I needed something that could be run by a single person. Hence a NDI PTZ camera and a 2nd monitor.
You can get away with an older CPU / gaming laptop... but you will be trading off $$ for better gear vs time to learning to optimize OBS. Would a 3 yr old i7 gaming laptop with an nVidia GPU most likely work fine? Yes. but be sure to do full length test to make sure of thermals. And learn to monitor hardware resource utilization to keep an eye on things
And then there is the whole online engagement (community) considerations
anyway.. lots of misc here. I'm happy to help out further.