Before you can start utilizing the power of Ableton Live in worship, you'll need some gear. This is assuming you have a basic sound system with a mixer board that has two free channels as well as in-ear monitoring, at least for your drummer. Here is a list of what I use and a brief explanation for each item. Click the images to buy the items on Amazon.
If you do not already have one, this will be the biggest investment for using Ableton Live. It doesn't have to be a powerhouse machine, but I also wouldn't buy a cheap PC that will crash on you half way through a song. I'm an apple fan-boy, so I would recommend a MacBook Air or Macbook Pro.
2. External Hard Drive
I recommend storing and organizing all of your backing track files and sessions on an external hard drive. Multitrack sessions are almost 500MB and could fill up your computer's hard drive really fast.
This is the first step in getting the audio signal from you laptop's headphone jack to your mixer board. The stereo part is necessary for separating the click track from you backing track into what will end up being two different channels on your board.
You'll need two microphone cables at whatever length suits your fancy to get the signal from the DI Box to your front-of-house mixer. Depend on where your sound board is located in your sanctuary, you will be plugging on end of these mic cables in the DI Box and the other ends in your stage snake or directly into the mixer.