There aren't too many phones that will survive unscathed short of the rugged ones (and those usually involve a lot of compromises). Nokia's Lumia 1020 and the Lumia Icon might take a beating, although you'd no doubt scratch them up.
As for Linux? If you have to ask, Ubuntu. It's arguably the easiest distro to try if you're new to the platform. Others tend to be either rougher around the edges or more specialized (you probably wouldn't want to try Slackware unless you were very comfortable with tinkering).