Assuming you want easy to carry and not a bunch of lenses to haul around in an SLR?
Sony DSCW800 is a decent one, has full automatic smile detec down to manual shiutter/f-stop for setting depth of field and point of focus. The lens on This one moves to provide 5x physical zoom, Then zoom levels after That are only crops of the center part of sensor.
These are pretty bulletproof, you can get them with 4k video, but fit/finish isn't sonice from no names, and the lens is digital zoom only, like cel phone just capturing center of sensor and making That
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If you want video, This will do 720p, A nicer one in your budget can do 1080p and have optical zoom in addition to digital zoom.
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For a Little More (Double), HD 1080p video is reachable in pretty proven systems
There are likely other s but those are two we use at the shop and have survived falls off an ATV onto concrete, so they're almost mechanic proof, not entirely but takes a lot of effort to break one.
Samsung option with full auto and manual mode and 1080pI'd suggest Going with a larger sensor SLR or video camera if primary use is 4k video.