After reading through this entire thread, I have a few comments:
(1) The OP mentioned about wanting to shoot photos of moving children. For this situation, with an A6XXX series camera, you are going to want native Sony or Zeiss glass that takes full advantage of the AF system. The Sigma primes (i.e. 16mm 1.4, 19mm 2.8, 30mm 1.4, 30mm 2.8, 60mm 2.8) referred to multiple times in this thread are all fine to fantastic optics when used with mostly static subjects but with the reverse-engineering that Sigma has done in leiu of buying the AF protocols from Sony, you will find the AF performance disappointing when shooting action, compared with native Sony glass.
(2) I see the OP debating between the A6300 and A6500. I would say go with the A6300 and invest the savings in glass because (a) there is virtually no difference in image quality between the two cameras; (b) good glass is a better investment than camera bodies as lenses retain their value over time while camera bodies are replaced every year or two by a newer model; (c) by the end of the year, both the A6300 and A6500 will be superceded by Sony’s newest APS-C model.
(3) If you do indeed buy a Sony camera, you can download a free version of Capture One, which is an excellent RAW processor. You can find free tutorials on YouTube.
(4) The Olympus system, mentioned by someone, is highly desireable due to an excellent selection of good glass. However, only two Olympus bodies, the EM1 and EM1ii, are equipped with phase-detect AF, so most Olympus camera bodies will struggle with shooting action. There is also the matter of the smaller 4/3 sensor requiring wider-aperture lenses to offset the effects of diffraction, poorer signal-to-noise ratio, and lower dynamic range.
(5) Even if the OP finds that zoom lenses better suits his style of shooting, I would still recommend buying at least one good quality prime lens, so he can see what the full capabilities of the camera are.