My personal $0.02. OBS Studio is a wonderfully powerful compositing tool, that is Free, Open-Source software (FOSS). FOSS implies responsibility on end-user to RTFM, take time to learn features, and somewhat self-support. If you want a support team you can call, that typically isn't free, and there are 'forks' of OBS Studio, and other software similar in functionality, that you can pay for and get hand-holding support. Just depends on your access to budget, onsite technical expertise, etc. Personally, I found OBS Studio to have a decent (to steep) starting learning curve, but once passed that, a joy to use. Though not available when I started, for a House of Worship (HoW), a nice guide book to OBS Studio would be
https://streamgeeks.us/obs-superuser/ which is a free PDF download, or print version is available for purchase.
There are those of us here willing to help out, as volunteers, to get other HoW users started. I'm sure there are for-pay consultants available as well.
If I understand correctly, you are talking about a single TV image, shown on 3 screens. Though, the number of screens really isn't relevant (as you will most likely take a single video output on your computer, go to a splitter, and send same signal to however many TVs (3 in your case). There are numerous technical/physical ways to distribute that signal... just depends on distance, cable routing options, etc. The question is whether the output to on-site TV screens is the exact same video to livestream?
The level of complexity depends on many factors. For our House of worship, I set up a single Ethernet (NDI) connected PTZ camera, audio via existing Sanctuary mixer, and PowerPoint for our Service Bulletin (which has liturgy, scripture, music, and more). And, based on our user community 3 years ago, livestreaming is via Facebook. And I documented setup, operations, etc for a couple of non-technical folks I've trained as backups to me (and have run livestreams when I'm out of town). I can add extra cameras easily.
- In our environment, there is a printed Service Bulletin handed out to in-person attendees. That, and some extra content, is copied into a PowerPoint slide show. A one-person OBS operator (on a dual-screen computer in choir loft) runs our entire livestream system, advances PowerPoint, controls camera, etc.
- For Facebook, I recommend using Scheduled (vs ad hoc) Video Event, so you get a consistent URL for every livestream, enabling folks to save that URL on streaming device (Roku, Apple TV, etc) and be able to watch livestream on their TV (which is what a material portion of our attendees do).
- Regardless of using OBS Studio, vMIx, or something else, the operational level of complexity will be fairly similar.
- And don't ignore copyright considerations, to avoid getting your stream blocked (again, has nothing to do with OBS Studio, just livestreaming in general).
- [added] and you can get started with same audio as using in Sanctuary, BUT livestream audio, to sound good, especially on mobile devices, requires a slightly different mix that front-of-house speakers. This is a next-level sophistication step, but be prepared for complaints if you don't have a plan to address this relatively quickly
I would say, that doing a decent (professional?) looking and sounding livestream for a HoW service will take some technical expertise to setup, regardless of the software chosen to pull it all together. But once setup, and operators trained, on-going operations isn't that complicated (but certainly not toaster style easy-to-operate, and I'm not aware of anything that is that easy, that also offers sophistication of flexible, multiple inputs as your are asking for). It comes down to what you want to accomplish, and who you have available to set that up and run it, and long-term support (like who will run livestream system if you are out sick, etc). And taking a look at what your HoW is already doing, and can be leveraged for livestream. Though it can seem overwhelming initially, Personally, my preference is to identify full requirements up-front, and then figure out what is practical with available resources. It may well be that what you want is more complicated than you/your church can support, but something simpler is totally doable? Or, once you (and your team?) step through a plan, that it isn't that hard?