UPDATE 2:
Now testing with Gobe ND8...and it's again interesting how it really changes things. The first thing I'm trying to fix is that the ND8 filter punches the shadows in (at any exposure) and is making them relatively darker than they should be (though this can be a good thing, if you're uploading directly to YouTube with the current compression scheme they have). Still working on these settings...

UPDATE: I’ve been working on getting my FZ1000 to look realistic, using SOOC (Straight Out of Camera) settings, and I’m pretty happy with what these settings now (and it’s REALLY EASY TO REMEMBER). These settings are mostly for 4K PHOTO mode use, so I'm also doing this so I can either use 4K PHOTO mode to grab stills, or to shoot video and be able to use it without doing color grading (though it may need a little sharpness adding in Davinci Resolve, my video editing software of choice…also super good for color grading). Note that the smaller sensor on this camera produces a little bit more NOISE than I would consider perfect, but it's not bad if you look at it as kind of an organic "film look".

(FIRST) NOTE:
This current test is for when you're NOT using a filter. The settings I had posted before were for using a B+W F-PRO UV filter, and I really prefer the tests with that filter (settings still available by searching on my website) but then it occurred to me today, that some people may not be able to easily get that filter. So far, this test is coming out worse, because using the filter was improving the micro contrast (it smoothed the highlight rolloff and did other good things). These settings are pretty good, but if you can get a B+W F-PRO UV filter, I think this camera works better with one.

SHARPENING SETTINGS (for Davinci Resolve):
@Full "WIDE" = .47 ?
@Mid "TIGHT" = .46 ?
@Full "TELE" = .43 ?

I should also note that I've found ISO 200 to create the most real-looking image (maybe it's the "native ISO"?) So, if you can use ISO 200, I do recommend it (even over 125 and 160, even though they're lower, etc.) Also, the image degrades noticeably above ISO 400, though I sometimes go up to ISO 800 when needed, but be aware that it's going to look like it has more "film grain" (which isn't always bad, but it won't match your other footage, if the other footage was shot at a lower ISO).