Options for Streaming:
Cameras. So many options here. You can use just about any HD video camera with an HDMI output but quality and features vary greatly. Same with tripods. It is actually harder to operate cheap gear. Start with your total budget. Do you have $10,000, $5,000, $1,000? You have to come up with a number. Consider purchasing tripods or other gear on eBay or other places. If you can find someone upgrading to new equipment, you can get a good deal on their old.
There are a lot of options for streaming/encoding. Software based. Hardware based. In my experience, it's always better to use stand-alone hardware products to stream or record rather than using a computer with software, (ie OBS, Xsplit, Wirecast, etc.) With a computer, there always seems to be something that slows it down. Screen savers, other programs running, failure to reboot, automatic updates, hard drive speed, dropped frames, etc.
For mixing video, I would use one of the Blackmagic ATEM Production Switcher products.
https://www.blackmagicdesign.com/products/atemtelevisionstudio/techspecs/W-APS-08
$995, 8 inputs. You can switch cameras on the front of the unit, and/or use their software control to switch inputs, fade up titles, dissolves, etc. Send a program output to monitors in your church, and to your streaming device. Some of the ATEM switchers include AUX outputs so you can send different video feeds to different places. Such as sending a camera feed to a monitor in your worship center, a 'dirty feed' to your nursery, a 'clean feed' to a recorder that doesn't include lower thirds, etc. The ATEM Switcher software has multiple tabs to control audio sources, media loaded into media players (stills or titles with alpha channel), camera control (if you have Blackmagic Design supported cameras). You can customize buttons and your Multiview. Very cool software.
Keep in mind that most of the BMD ATEM switchers require that all signals arrive in the same format as the switcher. So if it is set up for 1080i 59.94, then all cameras and other inputs arrive at the same format. It won't scale, but the on board frame synchronizers let you use inputs that don't need to be genlocked. You can use an UpDownCross converter to remedy this. Also keep in mind that if using cameras for IMAG in your Sanctuary/Worship Center, that there will be a slight delay because of processing. Genlocked cameras will reduce this latency.
Our church also uses a Blackmagic Design Smart Videohub to route signals to all the TV's in our building. We run SDI cables to all TV's. SDI cables from all cameras to the video switcher. Then convert SDI-HDMI at the TV's with converters powered by USB from the TV. HDMI-SDI converters from cameras that don't have SDI outputs. There is software control for this so you can route signals from your computer.
Our Worship Center iMac runs ProPresenter for our large projector and side screens. We split this HDMI signal with a distribution amp, HDMI-SDI converter and run that to our ATEM production switcher upstairs. We use an UpDown Cross converter from BMD to get it to the right format for our ATEM switcher.
For live animated titles and lower thirds, I use the SimpleSupers.com app that uses PowerPoint as a character generator. It generates an alpha channel. I use my laptop display outputs for key and fill into the ATEM's Downstream keyer. I use it for Lower Thirds at our church. Scripture, names, song lyrics, etc. I even use it to play out our intro and outro for our 'Sermon only' archive.
For streaming, I like the Teradek VidiU Pro and use it to stream to anywhere. This unit also records an H.264 video on an SD card if you want it to. Streaming to YouTube is free, Facebook is free. Twitch is free.
For one of my clients, I set the Teradek to stream to Restream.io and let it send out to about 18 streaming platforms with their free version. They say they have 30 free platforms they stream to. Although you have to pay to include streaming to Facebook on their site.
For recording I've had great success with the BMD Hyperdeck Studio Mini and the BMD UpDownCross converter. I use the UpDownCross to convert to 1080p and record H.264 on the Hyperdeck Mini's SD cards. Saves a lot of hard drive space recording H264, rather than ProRes or other Windows formats. You can use multiple recorders and record ISO's of your cameras, clean feeds, etc.
A cheaper solution is a stand-alone game recorder like this Hauppauge HD PVR Rocket Portable HD Game Recorder. $128. Records on USB stick.
https://www.bhphotovideo.com/c/product/1013313-REG/hauppauge_1540_hd_pvr_rocket.html
I input an HDMI signal from my ATEM switcher (converted SDI-HDMI) and it records audio and video. I set up the PVR first with my Windows machine and set the record data rate and anything else needed in the Hauppauge software. Then after that, it's a stand-alone recorder powered by USB. A cheap solution that's been very reliable for us.
If you want to save money recording ISO's, then you can use the BMD Multiview 4 processor and output it to a Hyperdeck Mini recorder in 4k. (You would have to record in ProRes or other format as H264 won't work in 4k.) This would give you 4, 1080 cameras on a single 4k recording. You could record Cameras 1, 2 and 3, then a Program (dirty) feed or 'Clean Feed' on the last quadrant. Put this 4k clip in your editing program in a 1080 timeline, and zoom in on the camera you want to iso during editing. You could set is up as a multi-camera sequence and re-edit your video if needed. This would give you 3 cameras and the line cut. Very cool way to save money in iso's and hard drive space. Or you could record an H264 clip with this recorder,
https://www.bhphotovideo.com/c/product/1137279-REG/video_devices_pix_e5_5_4k_recording.html.
God bless,
kc