What's the best video screen and sound capture software?

I’m about to train one of my clients, an artist who paints children’s art, in how to use the Content Management System (CMS), Order Processing, and so forth on her new Yahoo! Merchant Solutions Store. This includes a bunch of features I added that are not covered in Yahoo! help files.

I will have here store’s CMS open on my screen, and she’ll have it on hers. I’ll step here through everything she needs to know to manage and add/delete products, put things on sale, take them off sale, etc. Our audio connection will be via Skype, so she will have that as well as screen to capture, but needs software that can capture from the browser and Skype simultaneously.

She wants a video record for her own sake, and is also going to be bringing in a couple of people to help with store management while she creates new paintings, manages scanning of them, and giclee printing of them.

She’s on a Mac, but I’d welcome recommendations for Windows 7/8, or Linux, as I have clients using each.