I'm on the lookout for a new camera body and new lenses. I have come down to these 3 Sony cameras; Sony A6300, Sony A7 and Sony A7II. My question is, do these cameras have an itegrated AF motor inside the body? Or do I need to get lenses with AF motors? And also, do all E and FE lenses have AF motors? If not, which ones do in the sub $1000 price range?
Sony has made this super confusing by using alpha (α) —which is commonly rendered "A" — in the names of these E-mount cameras. (Thanks, Sony!) The current scheme seems to be: α followed by two digits = A-mount; all others (one digit, four digits, one digit and some letters, whatever) are E-mount. In addition to their "common names", these cameras also have model numbers which start with "ILCE", where the E stands for E-mount (and ILCA for A-mount cameras). The ones you list are ILCE-6300, ILCE-7, and ILCE-7M2, respectively.
All E-mount lenses have their own motors, so do not need a "screw-drive" motor in the body.
Some A-mount lenses have motors, but older ones do not. (I'm 90% sure that all Sony A-mount lenses with focus motors are labeled either SSM or SAM — if the description is missing this, look more closely.)
The E-mount bodies (like the ones you've listed) do not have in-body motors, but if you want to use A-mount lenses that require it, the Sony LA-EA4 adapter includes one of its own.
If you use native E-mount lenses — just as if you are a Nikon users with newer Nikon-mount lenses, or a Canon EOS user using native EOS lenses — this is a non-issue.