I don't hold with the differentiation between "Christian" music and "secular" music. What's good is what's good, and what's crap is crap. Most of what is produced on Christian labels is crap.
I appreciate music that makes me think and that challenges me to care about other people and that makes me stop and think about what I claim to believe. To that end, there are only three Christian musicians I've found that I consistently enjoy: Michael Card, Steve Taylor and Keith Green.
Keith Green died in a plane crash in 1982. His complete discography is available on Sparrow Records as "Keith Green: The Ministry Years." It's hard-hitting and prophetic stuff.
Steve Taylor is a former youth pastor who warranted an entire chapter in Jimmy Swaggart's book ranting about the evils of contemporary Christian music. Like Keith Green, his lyrics are also prophetic, but they're usually more in-your-face and are set to higher-power music than Keith Green's easy listening style.
Mike Card's music is more meditative and thought-provoking and often is Scripture paraphrased and set to music. I believe he is still rounding out his multivolume work on the Bible, which the last I knew merely awaited his album on the book of Hebrews. (I have a suspicion he's not going to follow my suggestion of rhyming Melchizedek with "Oh what the heck.") Mike's stuff is folksy, which I enjoy.
I guess I should add John Michael Talbot as a fourth Christian musician I've found I enjoy because of his meditative, worshipful approach to music.
Beyond that, I generally go for music that predates me by a decade or more, though not always. I enjoy Alan Sherman and Weird Al's wit (I'd also enjoy Tom Lehrer and Stan Freberg if I had their albums), but I also enjoy the folk songs of Simon & Garfunkel; Peter, Paul and Mary; and Crosby, Stills and Nash; and I enjoy a lot of the music produced in the 1960s and 1970s: Credence Clearwater Revival, the Beatles, and miscellaneous songs like "Eve of Destruction" and "Abraham, Martin and John." Billy Joel's music often is good also.
It really depends on what you want out of your music. Some music is nihilistic and embraces destruction, like stuff by Marilyn Manson, and other stuff just revels in offending parents, which I've never really found appealing either. A lot of what's produced today is meaningless fluff, but that includes a lot that's produced for Christian records labels as well. I used to get nauseous every time I'd hear the lyrics "God is too wise to be mistaken / God is too good to be unkind / So when you don't understand / When you can't see his plan / If you can't trace his hand / Trust his heart." (I feel sick just typing it.)
I've found much Christian music to be rather poor artistically and uninspired lyrically, which is why I don't listen to it. It's driven as much by the market as secular music industry. (Put it this way: How many balding middle-age men would make it big as Christian artists today if they were just starting out?)
I've found that the music I enjoy stylistically is simple and folksy rather than heavy on the synthesizer and electric guitars (Steve Taylor is an exception); addresses themes of lasting value, whether social issues like Phil Collins "Oh, Think Twice," or delving into spiritual matters like Mike Card or Keith Green; or telling a story of sorts, though such songs are rare these days.
The heart of the individual musician I'm never going to know. I don't generally keep tabs on musicians' private lives -- just not interested -- although sometimes it leaps out at me, as it did with Amy Grant and Gary Chapman's divorce. (Let me add that Amy Grant's "Lead Me On" album back in 1990-ish was her finest album ever, in my opinion, because it was so personal. I still enjoy it, even though the divorce foreshadowed in "Faithless Heart" has come to pass.)
Another example you can probably relate to: I'm aware The Beatles did major drugs at the height of their popularity, and I'm aware of the rumors that songs like "Lucy in the Sky with Diamonds" and "Being for the Benefit of Mr. Kite" contain veiled references to drugs. That knowledge does not alter my enjoyment of The Beatles' music, though I have to admit that most of the "Sergeant Pepper" album is a little too weird for my tastes.
We all have our own criteria by which we judge what music we enjoy and find acceptable. Like Dave Barry, I'm starting to hate albums with titles like "Classic Children's Songs from Hell." I'm satisfied that my tastes are in submission to God, even though I know some people who would pray that I would stop listening to Simon & Garfunkel.
As a side note, just because something or someone appears to be in opposition to the church, Christianity or even God does not mean what they have to say should not be heard. Many times people outside the faith have valid perceptions and criticisms we're blind to. Or as Cervantes once observed, "Even a fart can be musical."
Put your emphasis on the substance of the music and its style, not the label that it falls under. That way you can't go wrong, and if you do, it's not for lack of effort or for trying to take the easy road out.