I support "United Space Ship". The Making of Star Trek gives USS as "United Space Ship" and that "Enterprise is a member of the Starship Class". Additionally, The Star Trek (Writer's) Guide of 4/17/67, page 29 gives, ""U.S.S." on our ship designation stands for "United Space Ship" -- indicating (without troublesome specifics) that mankind ..."
In my opinion, this is supported by its original dedication plaque, "U.S.S. Enterprise, Starship Class, San Francisco, Calif." since it is redundant to put United Star Ship and then Starship Class to designate the same ship, so, it seems better that it is United Space Ship Enterprise, Starship Class.
Only after its refit was it referred as a Constitution Class which I assume is the class for the refit design.
In my opinion, this is supported by its original dedication plaque, "U.S.S. Enterprise, Starship Class, San Francisco, Calif." since it is redundant to put United Star Ship and then Starship Class to designate the same ship, so, it seems better that it is United Space Ship Enterprise, Starship Class.
Only after its refit was it referred as a Constitution Class which I assume is the class for the refit design.