United Star (or Space) Ship. Kirk used both interchangeably.
NCC doesn't stand for anything. The original idea was using N because all commercial aircraft in the US have an N number. The first C was for "commercial" and the third C was added for optical balance (NCC 1701 looked better than NC 1701).
Memory Alpha also states the the first C in NCC was in recognition of the Soviet space program.
http://memory-alpha.wikia.com/wiki/NCC
Memory Alpha also states that one of the Trek novels states NCC means Naval Construction Contract