The Nikon Coolpix line is very small, easy to use and fairly hardy as these
things go.
Things to consider:
Optical zoom: you don't want much more than about 4:1; anything longer than
that and your pictures start to get fuzzy because no one can hold the camera
steady enough.
Digital zoom: turn the feature off, or at least don't use it. It is better
to blow up pictures on your computer. Digital zoom is worthless; actually it
is less than worthless.
Movie mode: movie cameras do a better job, but it can come in handy now and
then. Sound is nice, but small cameras don't really do a very good job of
recording sound.
Megapixels: even a 3MP camera can take images that can be blown up to 11x20.
4 or 5 megapixels is ideal for most people.
You want to be able to turn off automatic flash and be able to manually
adjust your exposures to some degree.
Read reviews of the camera you are considering at
www.dpreview.com before
you buy. That site also has a nice glossary of all the technical terms that
get thrown around and what they really mean (as opposed to what a sales
clerk might think they mean).