I don't know of much in the way of "Christian Jazz"...it's not a musical style which really comes of an ideology, or is geared to express one; mostly jazz, like blues, is the playing off of timeless, original instrumental works. Clint Eastwood's rendition of "Accentuate the Positive" is about as close as you'll find to uplifting message in the body of classic jazz. There are so many "jazz sounds" out there that it's also hard to give tips on practicing jazz. All I can really say is that you is that listening to the great instrumental jazzers (Coltrane, Davis, Montgomery, Monk, etc.) will take you in close.
Theloneous Monk is certainly the best known instrumental pianist of jazz, although Gershwin also left a mark which was rooted in jazz but also extended into classical and contemporary.
What I did to learn jazz was by playing along with the instrumentals, and practicing modes (not just major and minor, but dorian, mixolydian, phrygian, lydian, etc.). Jazz will open you a lot more subtlety than playing in standard major/minor: intricate chords such as augmented and diminished 4ths, 6ths, 7ths, and 9ths will grant you the ability to express yourself in new ways, once you're used to creating phrasings which make use of those subtle differences in structure and voicing.
Once you master the style, you will be able to REALLY soar when playing contemporary styles, because you'll have all the key-changes down, and have LOTS of new techniques and chords to use, plus be fluent in every mode whereby you can morph smoothly between keys, and you can fill in by throwing in some blues, pentatonics, or harmonic minor during refrains, changeovers, etc., to break things up and keep it interesting.
I'd say practice the classical mainstays of the style: songs like "Autumn Leaves" and "Too Wonderful for Words" will tune you into the feel of jazz, and you can go from there.
