I now use only full-frame Sony mirrorless cameras (A7 series), but owned an APS-C A-6000 for a while. All of their sensors are really great, as Dennis points out. Resolution, color rendition, low noise, dynamic range, you name it, they hit all spots right on. They also have superb electronic viewfinders (once you get used to them you will never be able to use an optical viewfinder again) as well as very bright and crisp LCDs. Some people complain about their ergonomics, but I find them also excellent in this respect. They have a number of buttons that you can assign to the functions that you use more frequently, so that I seldom have to dig into the menu, but when I do I know exactly where to find what I want. In my view there are no such things as good or bad menu systems, it is just what you get used to. I recall that the A6000 did not have as many buttons as the A7 series, though, but perhaps some of the new ones (A6300, etc.) do.
Sony kit lenses, however, are awful. You get what you pay for. I would look at Sigma, they make some truly spectacular lenses these days. Or you can go for some of the high end Sony/Zeiss lenses, which are excellent but quite expensive. I do not use any modern lenses, though. All of my photography is with vintage manual focus lenses, mostly Leica, Zeiss and Minolta these days. I like their rendition a lot more than that of modern “digital” lenses. I also find the process of focusing manually (very easy on mirrorless cameras, with focus peaking and image magnification on both the viewfinder and LCD), and adjusting the aperture on the lens while actually seeing the depth of field, much more satisfying. For this reason I cannot tell you about AF speed, as I have never used AF on any of my Sonys. The A6000 is supposed to have very fast AF, and the new A6400 is supposed to be the fastest camera around, but I cannot comment on this. I also don’t know about out of camera jpg quality, as I have always shot raw and have never even tried the jpgs. They may be good or awful, I don’t know
Bottom line, if you couple any Sony mirrorless with the right lens and shoot raw the results will blow you away.
I hope this helps. Here is a link to some pieces that I wrote about these topics: https://fourbillionyears.org/category/camera-commentaries/