I got my girlfriend an ixus107 a few years back, its so easy to use, compact and takes brilliant snapshots.
Like all compacts you probably wouldn't want to print much higher than 12x8's or view at 100% in PS, but fir it's very modest cost it's great.
Got the mother in law an a4100 (or something, runs on lithium not aa's) same kind of spec and size and iq as the ixus, she loves it.
The current ixus equiv is the 127 which is on a few deals with case card etc.
The ixus 500 is chunkier and heavier. It's also a bit older and as I recall the zoom range isn't so useful at the wide end.
I have an sx230 for the glovebox and holidays. Nice enough cam, ok iq, good for a compact in fact, works great in green square auto, awfully cumbersome interface apart from that: too few butttons trying to do too many things. Even having used EOS cameras for 23 years and powershots for 12 years, and spent 6 years in camera retail, and being a full time camerman, I struggle to operate it properly.
So avoid the sx's.
The basic ixus has few buttons. Has good images. Is fairly inexpensive and a lithium battery with a decent life.
I would go down that route. The fuji's and the s powershots are way beyond what granny will need or want probably.