you should be all manual if you're shooting video, relying on anything auto especially on a A6k is asking for blown shots.
as far as one lens for outdoor use it doesn't really exist, but something closest to all all around lens on full frame is a 24-105mm, so the APS-C equivalent for your A6k would be ~18-70mm but not sure if something like that exists.
Also somebody above mentioned adapters but I'd highly recommend against that. First off you lose the size/weight benefit of your small mirrorless body, and they are significantly less reliable vs. using native lenses. The only reason to use an adapter is if you already have significantly invested in another lens mount and you need a crutch while you switch to native