I would go for a Nikon Coolpix 2500 or its successor the 3500. This was the first digital camera that I ever owned, and I still have it and like it.
2MP
3x zoom
No external zooming parts -- less chance for something to break
Lens housing rotates so you can get nice angled shots
Very simple and sturdy design
Compact enough to be handy, but not so much that all the buttons are tiny
Looks like functional 2500's are going on eBay for $20-$30. A 256MB or 512MB CompactFlash card is all you need for tons of photos, and you can pick one of those up for pennies nowadays.