Getting Started with Webcasting and Video conferencing
Blackmagic and Livestream are your friends :)

You probably want to get 3 cameras - one for the priest, one for roaming action shots and one for the audience. You'll need a whole bunch of microphones and an audio mixer. But you probably already know all this.

Buy a Blackmagic TV Studio and buy a Livestream Broadcaster - plug the TV Studio's HDMI output into the Livestream Broadcaster and plug a computer into the TV Studio's ethernet port. You use the computer to control the switching between cameras and the Livestream Broadcaster spits it out to the Internet using Livestream's servers. Make sure where you're broadcasting from has a fast Internet connection.

Lots of churches seem to have projectors these days, so you can plug the output from your projector's source (use a splitter of some sort, and a scaler to match the frame specs as the cameras) into the TV studio too, and add what's on the projector into the mix as well.

You can replace the Livestream Broadcaster with a computer, but the Livestream Broadcaster is cheaper, more flexible and more reliable, in my opinion. 

I guess this is a starting point - but if you want more info, just post and I'll answer any questions :)