Fifth, specialize in key of D. Really. You don't need 12 keys to do praise and worship, the guitars can't play more than 2 or 3. Get really good at D and you're ready for 90%. When you pick songs go for D or ones close you can easily rewrite.
When you say modern, are you talking about music that sounds like pop music? That can be hard to read if you're used to classical, because the rhythms and harmonies are different. But I think rule 2 will help. If you have time to practice, make sure you know the melody well, then the bass line, then the rest of it. If the chords are written with tricky syncopation, see if you can simplify it.