I'm looking into running my first campaign as a DM. What official adventure do you recommend to start with? I'll run it with new players. 

Please when you share your adventure please explain why do you suggest that adventure

Lost Mine of Phandelver. It comes with the standard physical set, so I feel like it's the ideal "New DM" module. It was the first one I ran, at least.

Probably Lost Mines or Dragon of Icespire Peak are the best for new DM's as they're geared at people new to D&D/new to 5e so they have lots of tools to utilize in learning how to navigate the game.

Don't do Tyranny of Dragons as your first module. It takes a lot of work to DM.

Quote from cosplaywrite >>

Don't do Tyranny of Dragons as your first module. It takes a lot of work to DM.

Seconded!  ToD duology is very...very...annoying to DM and play through.  It makes loads of assertions about player actions that either need to be thrown out or railroaded.  For instance how many times do the PCs have to enter the Bandit Camp near Greenest?  3? or is it more?  Why the FLIP do the authors do this?   I redid the entire thing as a MacGuffin Chase through the Western Heartlands!  Player Character's were hot on the trail of those dastardly Cultists and trying to investigate the whole matter whilst being usually a step or two behind.  Instead of slog, I reframed it to feel more like the Chase from the Two Towers as Aragon, Legolas, and Gimli tracked the orcs.

Quote from Hawksmoor >>

Quote from cosplaywrite >>

Don't do Tyranny of Dragons as your first module. It takes a lot of work to DM.

 

Seconded!  ToD duology is very...very...annoying to DM and play through.  It makes loads of assertions about player actions that either need to be thrown out or railroaded.  For instance how many times do the PCs have to enter the Bandit Camp near Greenest?  3? or is it more?  Why the FLIP do the authors do this?   I redid the entire thing as a MacGuffin Chase through the Western Heartlands!  Player Character's were hot on the trail of those dastardly Cultists and trying to investigate the whole matter whilst being usually a step or two behind.  Instead of slog, I reframed it to feel more like the Chase from the Two Towers as Aragon, Legolas, and Gimli tracked the orcs.

 Yeah, it's not laid out well. I wish I'd done my research on it instead of leaping headfirst into DMing it. (Bought it while I was still learning how to play the game last year because DRAGONS and didn't do enough research on how to start it before I leapt into DMing it from LMoP.) I've ended up eliminating large swaths of it. They took a long rest after fighting Cyanwrath at the start so I had the cult camp already abandoned when they got to it (save the prisoners from Greenest and Leosin). I've given them detours along the way to spice up the long slog north. We skipped Naerytar altogether because it no longer made narrative sense for them to find their way to it. (They also bypassed the mere entirely by sailing from Daggerford to Waterdeep because GoS came out right before we got to that session and I made boats available to them.)

I also am developing the lore of the masks more in-depth and giving the players chances to actually obtain the masks. (They got the green mask, lost it to the cult but gained the blue mask in the process by stealing it from Wyrmspeaker Galvan's dead body.) And will probably change it up that you need all 5 masks to form the full mask of the dragon queen since that never made sense to me that you only need 2 of them to form the full mask. (Will probably have it that you can combine any number of the masks but it won't have all 5 heads and thus not be the full mask.)

That's just scratching the surface of the changes I've made along the way. Though I wish I'd seen the suggestion to switch Phandalin in for Greenest if you're going immediately off LMoP instead of railroading the PCs down to Greenest to start the adventure. It would definitely increase the player buy-in if you're coming off the starter set.

Can't wait for 10/22 to see what changes they made to this set for the anniversary re-release.

I've also heard Storm King's Thunder isn't friendly to new DMs so I'd steer away from that one. If the starter set or essentials kit adventures don't ring your chimes for a first-time adventure, maybe try tales from the yawning portal. They're all standalone adventures, not a single campaign, but each adventure is designed for successively higher levels and you could easily link them by having someone at the YP to hire the PCs to go after the macguffin of the next adventure. By the time you get to the third adventure, you'll probably start feeling more confident in your own abilities to the point you feel you could devise more interesting plot hooks to link the adventures and turn them into an overall campaign.

Seconded for SKT.  Chapter 3 is not good for an inexperienced group, and as a new DM, you need to plan for a lot of different things or be good at flying by the seat of your pants.

For a first time DM (and for first-time players!), you'd really be pressed to find a better first 'canned' adventure than Lost Mine of Phandelver. There are so many reasons, but I'll try to condense:

1.  The adventure book is quite well-written for the DM. It provides a ton of guidance for running monsters and presenting options to the party. From the ground-up, the adventure was written for newbies.

2.  The adventure contains - a small frontier town in desperate need of fresh-blooded heroes and with a serious bandit problem; an evil spellcaster plotting trouble; two (count 'em, two!) dungeons to crawl through; and a mother-flipping dragon. It's classic pulp D&D, with a bit of everything you're going to want to use in future adventures to cut your teeth with.

3.  If your players aren't sure what kind of character they want to play (a novelty, I'll admit, but I've seen it), the game comes with pregenerated characters. If nothing else, let them look over the sheets so they can maybe be inspired by them to make their own. The game is a lot more fun when you're personally invested in a character of your own making, and you should encourage your players to do so!

4.  It's short! It's an adventure that goes from 1st to 5th level. This is a multifaceted benefit. First, there's nothing more satisfying as a DM than to 'close the book' on a campaign your players have been playing through for weeks, or months (or years!), and see them start excitedly talking about all the high points of the adventure, and what kind of stuff they're looking forward to in the next one. You'll get the chance to reflect on what you did well, what you want to work on, and what you want to do next. Next, 5th level is a big step up in pretty much every PC's power curve; it lets them get a really good look at what most of the D&D classes are going to start to develop into. Next, the players are first-timers; they're going to want to pull out pretty much all of the toys and start playing with them. A short first adventure lets them get to know a first batch of classes, and I almost guarantee that each of them will be playing something different in the next campaign.

These are the reasons I would suggest starting with Lost Mines of Phandelver. The important thing to remember is, that you need to find something that is going to inspire you to DM. Understand that no matter how straightforward the narrative of the adventure, it's going to require hours of prep time on your part. You need to stay ahead of wherever the characters are in the adventure, understand what (approximately) the players should be doing next, understand what NPCs around them want from them, and understand what the villain is going to be doing while the PCs are out being insipid interlopers. D&D is a great game, and being a DM can be an incredibly rewarding experience. But the book can't do it for you, and unfortunately the onus is on you to breathe life into the adventure, turn that book of text into a thing that lives in your players' memories. Have fun, and good luck!