First, I'd recommend recording. Wherever you livestream to (YouTube, Facebook, etc) will HEAVILY compress the video. It is nice to have a higher quality recording to refer back to. I'd recommend recording, then moving the recoded video to an Archive HDD after service is over. Having such a recording is also really appreciated for families with baptisms, weddings, etc.
With that said, I'd strongly advise on using NDI instead of any other video connectivity approach. NDI enables MUCH longer cable runs (in case you ever want to put a camera in front of the Sanctuary for an audience view. What you don't want is to mix connectivity approaches (USB or HDMI for camera closets to streaming PC, then NDI for distance camera, as you then are dealing with varying processing latencies, and trying to sync that.... no thanks .. not worth it. NDI is you more future-proof and flexible option. The downside is needing a basic understanding of networking to avoid problems. I put our streaming PC and NDI camera behind its own router/firewall, to protect it from the rest of the church network
I started livestreaming HoW last year with an engineering class workstation laptop and a single camera. Between OBS, using PowerPoint for Service Bulletin, monitoring livestream in browser at CDN provider, and NDI PTZ controls, a single monitor just didn't cut it. Don't forget about connecting microphone/audio system (mixer) to stream.
I put dedicated streaming PC tower in closet where we have our sound mixer. Did a little construction, and routed 15 meter DisplayPort and active USB3 cable up to choir loft area, and set up a 'streaming' station (a dual-monitor wall-mount with keyboard & mouse tray, that can lower to floor when not in use). By using DisplayPort MST, I can drive both monitors from a single video cable. By using high-quality active USB cable, no issue there either.
Now, you are asking specs, and as I'm not using your same setup, and you have mentioned what other CPU load you might have (ex ProPresenter, PPT, EasyWorship, etc) not to mention if you plan to use any audio filters? no way for me to guestimate hardware requirements. And then, you have to ask yourself, how long (in years) do you expect this system to last? Is computer expected to handle streaming in 4K in 3-4 years, for example? And being a single point of failure, what level service do you plan to get (ex. next business day onsite? have a spare system just in case, ??) For budget reasons, most Houses of Worship can't afford a spare streaming setup, so have a contingency plan ready
Hopefully someone else will comment on CPU/GPU impact with livestream + NDI output. Especially as you mentioned broadcasting to alternate local room (overflow, cry room, or whatever). And then there is how optimized the Operating System is for efficient operation (vs default settings... could make a 5+% (or more) CPU difference).
one option would be if that CPU load is too much on streaming PC, you could take OBS Projector or similar and use long video cable or use converters to route over Ethernet. Another option would be, depending on bandwidth considerations, is to have alternate room simply watch the livestream. For us the typical 'delay' is only around 15 seconds, so depends on if a 'cry (baby) room' with window into Sanctuary listening to live audio, then a delayed video wouldn't really work. But into a room with no view or direct audio from the Sanctuary, using livestream would be fine (and therefore not impact workload on streaming PC).
The issue in my mind is timing and does it really need to be a laptop. I'd much prefer a AMD Ryzen CPU and nVidia RTX CPU, but getting that with USB4 or Thunderbolt is (near?) impossible. As for Intel Alder Lake, the mobile CPU won't be out until next year. basically... sucks to have to buy a laptop now. From what I've read here, the nVidia Turing vs Ampere NVENC isn't that much difference. Where RTX/Ampere would make a difference, I'm guessing, is if you went to use RTX noise reduction (but recent CPU impact comments say beware of using it in prime time??). I say this as a GTX 1660 Super or better may suffice for 1080p30 GPU encode offload for you. What I'm not sure of is which NDI driver/toolset you plan to use on streaming PC and whether that can use GPU for decoding, or if receiving NDI signals have to be entirely decoded in CPU. And then you have companies like Panasonic, with their VirtualUSB driver that takes their NDI cameras and makes it available on PC as though it was USB attached (avoiding any other NDI drivers/plugins, etc). I don't know about other NDI camera vendors.
I suspect any GPU with Turing or Ampere NVENC will work for you. And you'll be better served in the long run by going with a lower GPU in that range and putting the savings into the CPU
