My vote goes for PeppermintOS http://peppermintos.com/
It's very light, as it uses the LXDE desktop and web apps by default .. but it's NOT just a "cloud" distro .. you can install any application locally too.
Think of it as a kind of "minimal install" distro, that through the use of web apps is still fully functional out of the box, at NO cost in system footprint .. then you can add just the local apps YOU want, not someone else's choice
It's based on Ubuntu so has access to ALL the software in the Ubuntu repos.
For transparency, I must add I'm a member of "Team Peppermint" .. so you might want to listen to what distro's others suggest before deciding to listen to just my advice
Meanwhile, there are some Peppermint 4 video reviews for you to have a look at here: