Yes, the 3 cameras go into a switcher, some switchers have some graphics capability in them, most don’t, so if you wanted to add title screens, lower-third supers, (you know, things like the chapter and verse at the bottom of the screen while talking about a bible passage), you’d need a fourth source, apart from the 3 cameras, to supply the graphics. That could be something simple like a laptop with video-out, running powerpoint slides, or a full-blown character generator, or anything in between. It mixes into the switcher just like the cameras do. The switcher then outputs to a monitor for you to see the final live mixed signal. Your audio runs separately in most cases, from an audio mixer to the inputs of your master recorder.
Some switchers like the Video Toaster, Newtek Tricaster or Sony Anycast, combine literally everything into one box, the switching and effects, the audio, the graphics, even recording to a hard disk and internet streaming. Of course you pay more for that. Cheapest Tricaster I saw (comes in three levels of cost and size) was just under five grand. But it’s a complete portable TV station in a box essentially, just add cameras and go. Pretty popular with churches and the like.
I was at a Walmart the other day (against my will) and saw analog DVD recorders without a TV tuner, just analog inputs, going for around $60. This would be perfect for you to burn a live DVD master copy from the output of your switcher, up to 2 hours long. You then would use a computer or stand-alone DVD dubber to burn additional clones off that master DVD. That’s the fastest, most efficient way to do it. For duplicating small runs of DVD-R’s, I like the Bravo Primera Pro. Makes a 2-hour copy about once every six-ten minutes, with printed label.
When buying the stand-alone DVD recorder, it makes sense to spring for one that also has an internal hard drive that can record simultaneously. What that does for you besides having a backup to the blank DVD itself is it lets you make additional DVD copies in that machine, faster than real-time, and even do rough editing in the sense that you can use the remote controls to copy over only the segments you desire, by setting in and out points. It’s like setting up a playlist on an ipod, not all that hard to do. You may also be able to set chapter markers on the fly during recording for main sections of the service, so people can skip right to the part they want.
The cheapest switcher I saw recently was just under a grand at B&H for an Edirol brand, kind of targeted to disco video VJ’s and perhaps smaller churches. You’ll want to select a 4-input (minimum) switcher that can automatically synchronize any analog video input, look for mention of that feature somewhere in the documentation.
I imagine how you’re going to shoot is with the cameras somewhat distant from each other and running the analog video back to your switching station on composite BNC or S-video cables. Cheaper than firewire and longer runs that way, though quality may be somewhat less. But those sources need to be synchronized or “timed” to make them work with the switcher. Most modern switchers have the hardware for this built-in, but be sure to check for it, this is a deal-breaker.
I’m not sure by the flavor of your original question that you are quite ready to dive in this deep. If you have cable TV in your community, it would be useful to sign up for a production course at their Local Access channel. You’ll get free or low-cost training on all this type of gear, so you’ll be able to make informed decisions on purchases later as well as know how to hook up and use what you’ve bought.