We don't know what the exact mission of the ship in the actual, aired version of "WNMHGB" was. We do know Kirk considered it his duty to enter the exotic phenomenon blocking his way specifically because the route had to be assessed for future users; perhaps an immediate safe return would have met all the mission objectives.
Interestingly, the ship had a psych specialist aboard, a seemingly unusual occurrence. This might suggest a short there-and-back sortie, so that Dr Dehner could report on her findings - or an exceptionally long extragalactic journey where Dehner's expertise would be vital in keeping the crew functional.
Most of the crew appeared very young, too - the skipper in particular. This might be taken to indicate a multi-decade journey where Starfleet's most expendable would spend their best years, achieving things Starfleet's most experienced never could.
To nitpick, though, this probably wouldn't count as a maiden voyage by any stretch of the term, as Kirk wouldn't be the ship's first commander. But in the aired version, we can claim that the ship was extensively rebuilt for the extragalactic sortie and was a space virgin of sorts in that sense - whereas the log quoted above would seem to lack reference to such a rebuilding.
One need only travel up or down (relative to the axis of the Galaxy) to reach the barrier.
Considering the curious shape of the barrier, one would suspect a very specific heading is needed to reach the exact spot where that purple ribbon can be found... The rim of the galactic disk would be an intuitively plausible candidate for that (insofar as such a disk really exists - but perhaps one does exist in terms of purple ribbons of weirdness, even if not in terms of stars, dark matter and other real-worldly stuff).
Going above or below it would be an option, then - but as said, Kirk seemed to consider it his duty to go through instead.
Of course, we may argue that the purple ribbon would appear smack in the middle of the flightpath regardless of the path; perhaps it's a polarization phenomenon of some sort for an envelope that actually extends in every direction. Or then the sky at the "rim" is littered with those purple ribbons and one will be hard put to find a hole between them - but only the very nearest one will be visible, and perhaps then only through visual enhancement techniques that serve both our heroes and our own TV sets.
It's certainly a curious phenomenon by any standards, and a worthy goal for an exploration mission. But one probably wouldn't send a ship on her maiden voyage to such a demanding assignment.
Timo Saloniemi