Chromebook Recommendations

Ok, so I’ve been one to deter from chromebooks for quite a while now, due to the fact that you can’t really download anything. Currently at home I have a desktop and a gaming laptop and as of right now I’m really interested in Chromebooks. My budget is $350-$400. Certain things that I am looking for is a 13.3 or 14’ 1080p screen. Additionally, I want something that I can install Linux to it with no problem. I am also a commuter and that’s the main reason I want this chromebook I want something light and portable and must definitely have a good overall battery life. Other than this that’s basically all I’m looking for. I would really appreciate any recommendations right now.