Your options are pretty much limited to Ubuntu distros unless you don't mind spending hours configuring firmware. MY personal favorite is Lubuntu. It's a really slimmed down minimal distro with LXDE., Super memory/cpu efficient.
Seconded Lubuntu is a great linux distro for your battery. The one thing that annoyed me a bit, when I used to use it, was the keybindings was not in the settings, and you had to go to some file and add them. Not sure if it is still this way, as that was 3+ years ago.