Goals
These were the unofficial goals, NOT in any particular order!
The equipment and process used for publishing the sermons is quite inexpensive. We needed to make it EASY to record the sermon, regardless of who was running the sound system. There are many methods available using PCs, but the physical space we had was very limited, and a PC comes with its own complications (how to start, run, what kind of application, etc.)

Equipment
An outboard USB audio device helps with our laptop; there are a variety available, but one with line level inputs/outputs is very useful. We stream our service using the free streaming offered by caster.fm. Two reasons caster.fm was chosen:
1) Free service offered
2) No 'in-stream' commercials

We use a laptop running a version of Linux, and use BUTT (Broadcast Using This Tool) which works great with caster.fm
BUTT also offers a recording button. This lets us record the stream (just the sermon), and then do the post-processing using Audacity.

We hope that you find this information useful.