First time DM here, running this campaign.
1) It's actually a blast. I've found that the campaign is a great "scaffolding" to build on: add your own flourishes, build NPC backstory and surrounding lore to make the world feel deeper and alive.
2) Have fun and add your own flourishes, and more characters if you want, to Phandalin. It doesn't take a lot of description to make a character work—a look, a quirk, and a goal seems to do it. I randomly added another merchant to Barthens provisions—an out of place and talkative Chultan—who argues with Elmar all the time, and the characters loved it for some reason, and now they are always going back there for advice and gossip.
3) Take it slow. Try not to look up rules too much—flipping through the book can kind of kill the vibe. If you've got a question about something, come back to it after the session and learn for next time.
4) Don't pull back the curtain.
5) The weakest part of this adventure is the lack of detail on the black spider. Use your imagination and have fun making him more of an ominous villain.
It's a blast. Have fun!