So, I managed to run a couple of short sessions of Lost Mine of Phandelver for our band of adventurers, and I like to think that (hope), everyone involved had a good time. The party managed to survive a goblin ambush (although two characters almost died), and were able to track the vermin back to their hideout. Once there, the PCs fought more gobbos and their bugbear leader. In the end, the heroes managed to win the day and even rescued a fellow adventurer. There were a few more encounters in and around the area known as the town of Phandelver.
I won't bore the reader with a detailed accounting of what transpired for the remainder of our gaming sessions (in total, 3 sessions), other than fun was had by all and no characters died. D&D 5e is fun to gamemaster, has the feel of old school gaming, and I definitely plan on running a campaign of my own when I feel the time is right.