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SchoolForge is a directory that contains Free Open Source Software (FOSS), including educational software. For each application on site, the platform(s) it runs on; Linux, Windows or Mac, is clearly marked. For kid and family-friendly games, keep MyGameCompany in your bookmarks, which screens the game titles for violence, adult sexuality and foul language and distributes the games that can pass through this screening process.
Finally, as you will be providing technical support for your kids (at least at first; they will learn how to fix things in a very short time), it’s useful to have a remote access program that supports Linux. YuuGuu is free and Linux friendly and you can set it up pretty quickly. If you are a tech-savvy parent, consider VNC.
Depending on your kids' ages and depending on your computing resources, you may also want to give Doudou Linux a try.