Tenor is an awesome sax to play in church!! You have to be careful about over blowing. The tone in the upper register can go out of tune quite a little bit.
When I play tenor, I try to think about long smooth lines and phrases. It is a bit more mellow in most cases than the alto, however I have been known to tear it up on tenor during a shout chorus.
The reason why most people play alto or sop is because the pitch is higher and it can be heard better. Just remember to relax and really work on getting a good sound out of that stove pipe.
Long tones, every day... Scales, every day, full range... Arpeggios, everyday, full range. In all 12 keys.
Start things slowly then progress in tempo as you get comfortable. I promise you that if you take the time to learn some fundamentals, your playing will soar ahead.
Feel free to PM me if you need some more ideas. I teach jazz, funk, theory, and classical saxophone to about 30 students right now. I enjoy helping people out!!
Peace,
Wolfram