Some questions I might be interested in finding answers to:
* Does this church have large number of single people in their twenties and thirties?
* How intellectual are the sermons?
* What, overall, are the priorities and personalities of the people who attend there?
* What does the church think about [women pastors|gay marriage|etc.,etc.]? Does everyone there agree?
I would suggest looking at OKCupid for ideas. OKC, as with all online dating, has its faults -- but it is good at figuring out what you are looking for and then showing it to you. Such a model might work here, as most churches don't share a dater's desire to be selective.