Broadcasting used to be the domain of only large churches. I remember attending NAB in the early 90's where I was told that it was more cost effective to pick up each viewer of a local church service in a limo and bring them to a church with lunch afterward than it was to broadcast a sermon. (No idea if that anecdote was true, but the point is that broadcasting to network quality is expensive).
Luckily, internet streaming came along and churches could use their existing IMAG cameras to take their services online. Yet, streaming isn't 100% accessible. You still need an analog-to-digital converter as well as a live streaming provider.
But this year, the next revolution in broadcast accessibility just became available. Two applications--Periscope and Meerkat --allow users to stream video from a tablet or smartphone. These two applications aren't the first to try this, but the difference is that with more 4G mobile networks and the ubiquitousness of open wi-fi , this time, it looks like personal live streaming will stick.
Meerkat launched this year at SXSW followed shortly by the news that Twitter had acquired Periscope.
Use is fairly straightforward. You download the app and either set up your login or--in the case of Periscope--sign in with your Twitter login. Then you can either watch a broadcast or start a broadcast. To view what you are broadcasting, others have to be on the platform. You have the choice of limiting your broadcast to "friends" or making it available to anyone. You also have the choice of enabling notifications so that you get a message when your friends are broadcasting.
The barrier to making this truly useful in churches is that it requires socialization of the technology within a congregation. The church would need to decide which of the platforms to use, then promote it so that people know to download the app and know when to look for the streams. This is not YouTube or Vimeo--which both play archive videos. These apps are designed for live broadcast. Think FaceTime, but to a larger audience.
If the idea appeals to you, grab some friends and experiment with the technology. Then, if it looks like a good fit, take it to a larger audience.