I'd agree, a native 9.3 in-the-box phone is best bet if you can find one.
I only upgraded from 9.3.5. 9 days ago on a 6S+. An older version (can't recall) of iTunes didn't recognize the 10.3.1 release, so iTunes had to be upgraded first (to 12.6.0), and this may have been due to the signing issue.
If you can't find a "9.3" iPhone in the box, an older version of the firmware and iTunes may be an option, no guarantees, to get around the signing issue.
A possible direct link to iTunes 11:
http://appldnld.apple.com/iTunes11/0...nes64Setup.exe
There are Apple serial number decoders. If you find a non-refurbished 6S, running the serial number through a decoder may give you an idea of the Date of Manufacture, and from there, you'd know if it was boxed before IOS 10 was released, which seems to be reported as September 13, 2016. I've used everymac in the past:
http://www.everymac.com/ultimate-mac-lookup/
If you seek a 6S, also check the serial number here:
https://www.apple.com/support/iphone...ectedshutdown/ to ensure it's not one with a battery issue. If it was sent back, even if free service, I doubt it would come back with less than the current version of iOS.