Rosie, good to hear everything went well. Your commute will soon turn into the favorite part of your day, and you'll start finding the long, and very-long ways to work... :P
My commute use to be 20min/15 miles... On the way home it can sometimes turn into 150miles - 2.5hrs....
Like on a Friday afternoon or something.... Good thing the twisties are so close....
Anyways, concerning the neutral thing, let me share my experience. I have had a lot of false neutrals on the bike, and after analyzing all of them, I find they're all user error. Not pointing the finger at you, simply sharing my own mishaps. I've found if you sit with the clutch in, at a stop, and you're not already in the gear you wish, the transmission stops spinning completely, and has no momentum to be able to engage a gear with. If you find yourself in this situation, letting the clutch out for a hot second, and then shifting usually does the trick (this is equivalent to rolling the bike forward or backward), either way your spinning the gears in the transmission, which allows the gears to engage.
To battle this issue (and because I'm beyond lazy to hold the clutch in through an entire red traffic light), I usually shift to neutral at a stop light and let the clutch out. To get going I pull in the clutch, shift, and rock off... So what ever you're comfortable with.
And yes, it is probably safer to leave the bike in gear, with the clutch pulled at an intersection so that if somebody doesn't stop in time, behind you, you can scootch forward to avoid an accident, but whatever you feel comfortable with.