Basically if you have a king james bible of any publisher you have the real thing. However if you have a new king james bible or a Children's king james version or a 21st Century King James Version then you dont have a king james bible. If you have any other english bible than the king james bible then that bible is not worth reading.
Below are the king james bibles that I recommend. These bibles I recommend below are as far as I have checked not counterfeit.
1611 King james bible from oxford
AV1611 bible, that is a bible that is identical to the original king james bible published in 1611 with the chapter summaries etc. The only difference is that its roman fonts so that its readable. This is a very good bible in my opinion and its the bible I read every day.
KJV Large Print Text Bible Hardback from Cambridge
This is a hard back, font size 11. Good enough for reading unless you get tired.
KJV Large Print Text Bible leather from Cambridge
This is a leather fine bound bible with font size 11, same as the hardback above. Good enough for reading unless you get tired.
Windsor Text Bible hardback from TBS
This is a hardback cheap but ok bible from trinitarian bible society. Font size 9.6. Cheap but small text.
Extra Large Print Bible from TBS
This is a large text size bible from trinitarian bible society. Font size is 15.5. Its kind of a pulpit bible. Good for people who cant read small text.
1769 New testaments
Giant-Print New Testament from Cambridge
This is a new testament only giant print hardback from Cambridge. It has font size 22.
Non English Bibles
Regarding recommended non english bibles. I guess God would create one bible in each language that is correct so there should be a correct bible in each language. My guess is that that bible would be made before 1880 and would follow the king james bible text. There are those who have done studies on possible bibles in the other languages. Here is an example.
It is available in digital format at bibel.com both as an mobile app and desktop. The bible version is there called SK73. You can also download it within the mobile app to your phone and use it offline on your phone. The app also exist for Ipad.
Its also possible to buy it nowadays as a bible that you can read in your sofa.