I agree that operations are extremely important and most churches work off volunteers. But that's why I still recommend digital, especially for the price point.
1.) you set the board the way you want, and then you create a backup. If someone messes something up you load the backup. You are up and running in minutes.
2.) ability to change individual setting on the fly. Say you have a rotation of 5 guitarists all with different gear, different pickups. You can save all of those EQ settings to presets and recall them on the fly.
3.) Ability to have compression, EQ, gating and reverb on every channel, built into the mixer.
4.) iPad control for when you want to run sound on your own rehearsals or if the sound guy is sick that day.
5.) Digital snake makes setup a breeze. My church is a multi purpose facility we literally have to tear down everything after a rehearsal. Setup and teardown can be done in under 20 min, it would probably be an hour with having to deal with analog gear.
On a side note, yeah be very careful of fly by night companies who will do sound setup. Do research in your area to see which ones to work with. Get a list of clients they have helped and talk to them if they were satisfied or not.
Sounds like the company you dealt with just wanted to sell some A&H gear. The more reputable sound system companies will work with anyone, will work with the churches budget and know where to get the most bang for your buck. They should also do a total sound system analysis for free. They should be able to tell you if you have adequate power for your speakers, adequate speaker coverage, they should do an audio analysis of the room and make sure the speaker placement is correct, in addition to just being able to sell you a board. If you just want to buy a board you can go to Guitar Center for that.