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To find a video camera with the wants above at that price point is near impossible, but a M4/3 or DSLR with some research may be your best beat that way you can change to faster lenses.
Overall, I have to disagree with that. I have some reservations about the "a6000" which was designed before "hybrid cameras" (still cameras with strong video capabilities) became a recognized market, but the Panasonic G7 is a highly regarded video platform for Full HD and for 4K. The only reservation I have for the G7 is the low light capability, and even there, it is only relatively "weak" when compared to the latest Sony A6500 and some of Sony's "full frame" cameras, and that can largely be corrected later by lens selection (using good primes on an "accelerator" adaptor).
Granted, the $500 price I posted above only leaves another $150 which would not be enough to cover a good quality accelerator + prime, but the interviews would be well covered for now. Actually, you could put the $150 towards a good mic. The G7 does have a mic port.
"A6300 VS G7 (gh4) - 4K Detail and Lowlight Comparison"
posted by "Max Yuryev", Mar 1, 2016
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NOTE: The Sony a6300 is a high model than the a6000 and costs much more. As I wrote above, the a6000 does NOT record 4K. But at Full HD, as far as I can remember, the a6300 was not very different from the a6000 for low light. You should check some reviews about that, say, DPreview and Imaging Resources, but that was my impression.
"$447 vs $3500 - 5D Mark IV vs G7- 4K video compared!"
posted by "Max Yuryev", Nov 23, 2016.
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This is just another look at the G7 in another comparison. It is a very good video camera even just for Full HD. But it is a particularly good buy for 4K at the current price.