Bless your heart Ben
The size of the panel and the conductors ran to it would depend on the calculated load that is being installed.
To ask about 3-8 cable in nothing more than a guess as to what the weather is like on the other side of the universe.
A couple of things that I can answer are;
Yes you would need to install both a grounded (neutral) and an equipment grounding conductor with the ungrounded (hot) conductors.
You made the statement that the church has a three phase service and the number of ungrounded conductors would depend whether you are installing a single phase or three phase panel.
No the panel will not be required to have a main disconnecting means but it is very advisable