The most important for me is least shadows on faces on sunny days.

When we travel, I like a small pocket camera, with me all the time. Clear photos, with accurate color are really important. In this modern age, most settings should be automatically adjusted by the camera. No necessity to remember to set this, or that. 

It will be great to play HD movies directly on the TV too. Any suggestions which of these 2 would be best? I have researched a lot and these seem to be best to get rid of sun shadows on a subjects face. No other company advertises 'superior auto', designed to lighten sun shadows. I appreciate all experiences on the subject.