I'm surprised you haven't had any replies from someone familiar with this type of production, but since you haven't, I'll at least try to point you in one possible direction..
I Googled this phrase, "live video mixer church services" and one of the links I got was:
http://www.videouniversity.com/switch.htm
They list several equipment package choices and one has a mixer for under $1000.
You might also try checking older posts in this topic.
When you get things setup, why not post your experiences here, to help those who will follow in your footsteps?
Good luck!