Note that any modern camera (except maybe for high end professional gear like Hasselblad) do have a fully automatic mode. The point is more how much options does she fancy to worth the price or does she rather put everything on best lense / ccd?
Compact is nice you can take it anywere but what Mike Peat said is true. My first camera was a ultra simple compact film camera ( indeed bought without inquiring my photographic ambitions) and yes the camera was mostly a disapointment. Ofcourse with digital cameras there is no film waste/cost and most digital cameras have more fun options than a 'al cheapo' pocket cameras in the 70' (oops I gave away my age;-) But the small cameras tend to be battery junkies.
At the other end there are not so compact cameras with a lens with quite some diameter. Most times this means better image quality (and higher price).
Next some cameras are quite slow with shutter response (which is awfull if she like to shoot pictures of friends)
You may also want to browse through 'choosing a digital camera' http://www.shortcourses.com/