hi
Most digital cameras from reputable manufacturers, nowadays, are very good, so I would set yourself a minimum standard for resolution, memory & optical zoom & after that base your choice on the price & any other features that appeal. Canon have always had good reports & our little Ixus 400 has been fine for us, the newer ones are even better.
Personally I wouldn't buy a camera online, I want to be able to pick it up & see how easy it is to use, some of the smaller ones can be quite fiddly, so I would recommend going to a local specialist shop. It may cost a little more, but, in my opinion, you get that back in the extra service (and advice) a local shop will provide.