I use the Logitech MX Anywhere mouse.
I can't give much of an arthritic-hand specific reason for why I prefer it, really. It seems to fit my hand a lot better than most other mice, and it has a nice weight to it. Also, the buttons on the side are very useful for going backwards/forwards on a browser tab.
This is a great mouse for 38 quid. Works on glass. The full size version is £40.