Awesome idea. Audacity is easy to use too.
KidPix software has a recording option and you can add pictures or text. Easy for younger ones.
Check out The Voice version of scripture. It's laid out like a screenplay in contemporary translation. It's one of the version options at www.biblegateway.com. A good start for a script.
UPDATE 1:
Plug a "big" microphone into any iPhone or cellphone using an adapter.
They even sell inexpensive mikes with adapters: click to enlarge
UPDATE 2:
Google "free Audio editing app for iPhone"
There are several that allow you to stitch together various files and cut out parts you don't want to use.