My group uses a private Google+ community to organise the games, and G+ alongside Roll20 to play the games. We play entirely online on a weekly basis, mainly because we're all about the same age and have small children and families, so it's difficult to get together for a face to face game.
For D&D 5th Ed you're pretty spoiled for choice, but when it all boils down the best two options are this:
Roll20, either in conjunction with G+ or on it's own. You can create an account and run your campaign through it for free, and the biggest pro (in my opinion) was the ease of use when it integrates with G+. Most everyone has a google account these days, so they also have a G+ account whether they know it or not. Once you've created your game in Roll20, you can choose to launch it in a g+ hangout.
Once you've done that for the first time, whenever you launch a G+ hangout the Roll20 app will be present, and you can launch it and select your campaign from within the hangout. Running the game each week becomes as simple as scheduling a G+ hangout event and showing up - the players don't even need Roll20 accounts, they just click the hangout invite link and game on. The D&D 5e character sheet for Roll20 seems pretty excellent too, with some dice rolling automation built into it. We're taking it for a test run soon hopefully.
The other main option right now, though it can get pricy, is Fantasy Grounds. It's not as simple for the players as Roll20 (which is, as i've said, just a link click), but if they're willing to install the program (available on Steam now as well), Fantasy Grounds is now the official online tool for D&D 5th, in partnership with Wizards of the Coast. It has excellent integration with the rules system and character sheets, as well as supporting hero lab. Some friends of mine swear by it, though it is a bit more complicated to get set up and running.
Both solutions support full voice, and I know Roll20 supports full video both in the app itself and through hangouts, as well as an online tabletop for maps, images, handouts and whatever else you like. This made it a lot easier for us to retain that "social tabletop" feeling, despite playing entirely remote. Using a large enough screen and a good set of speakers and microphone, you could play partial remote (with only a few players remote) or even with everyone in the room and disabling the voice and video altogether if you wanted.
Either way, if you do plan on getting in to running your games online through virtual tabletops, Google+ is your friend! There is a massive community of people there who will be more than happy to lend any assistance required.
Personally, I run a community geared at assisting people to set up, run or find games in the asia-pacific time zones. You can find it here: https://plus.google.com/u/0/communities/100566740249118526694
For other timezones, such as the American zones, a great place to start is here: https://plus.google.com/u/0/communities/107422815813208456454 It's an excellent community filled with friendly people.
How should I go about choosing an adventure for a group of new players?
The most important thing is to find something that speaks to you. If the premise leaves you flat, you are not so likely to be able to breathe life into the campaign.
The other most important thing is to find something your players will enjoy. Heck, they'll probably enjoy anything you DM cuz you'll be so great, but if they are all obsessed with dragons, maybe the module with the dragons, right?
What qualities should I look for?
Make sure the module you select is for new first level characters.
(Unless you really want to start at a higher level, which would make
your work a bit harder.)
Modules labeled introductory are good for starting DM's and players.
They often reprise the rules you will need to be familiar with, and
give points to where to look rules, etc.
CAVEAT: The word "introductory" doesn't have a fixed definition. Some introductory modules will be entirely self-contained, while others might require other materials, such as the Monster Manual and the DM Guide.
A module might be (A) specifically for particular game rules (like
D&D 5e), (B) be "compatible" with a set of game rules, or (C) it
might be just the "story" part without the monster stats. A module
of the first type will be easiest to use.
...and how can I tell if a published adventure has them?
I think that a trip to your Friendly Neighborhood Game Store might serve you well. The staff of typically pretty knowledgeable, and you can flip through the merchandise. Other customers often might offer their insights as well.
This site and others have chat forums where you can get suggestions and discuss.
You might also read product reviews online. For the in-depth info you are interested in, I'd favor review website like Escapist Magazine over reviews at online stores (although both have their place).
Should I restrict myself to official WotC adventures on the presumption that they have the best writing and playtesting or is there a way to identify third-party adventures with a similar (or higher) level of polish and quality?
Probably not a bad idea to favor the WotC's D&D 5E material, if that's what you're going to be playing. This has more to do with the encounters being tailor-made for 5E, than one company's material being better than another.
So which are those?
Applying my own answers to your criteria, The Lost Mine of Phandelver in the D&D Starter Kit, and Tyranny of Dragons both would be solid choices. Phandelver also would be a good fit for the number of play sessions you mention.
Tyranny of Dragons is an updated version of the early D&D 5e releases: Horde of the Dragon Queen and its sequel, Rise of Tiamat. Its updates include play balance fixes, perhaps most notably in earliest set of encounters, which make this module more appropriate for beginning DM’s and players.
NOTE: More recently, another official introductory module has been released: Dragon of Icespire Peak. I haven’t read through this one yet, so I cannot comment on its specifics.
You'd mentioned social encounters...
Most D&D modules have a whole lot of fighting involved, and the two I mentioned are no exceptions. Without doing any spoilers, Phandelver probably is more dense with opportunity for social encounters than Horde of the Dragon Queen.
The existence of opportunities for social encounters, of course, has a lot to do with your DM'ing. Monsters don't have to attack the party on sight, even if the module says they do.
Best Answer
Be prepared to tutor them in the rules.
Much like video games have "tutorial" levels that are basically an exercise in playing the game, you will need to set up situations and encounters that are simple and actually walk them through the rules a few times before they can be expected to master them.
Make them accountable for knowing their own characters.
Characters in D&D have many special powers, spells and magic items that all have unique powers and uses in as many different situations that all have to be reconciled with each other. As a DM, you are responsible for adjudicating how these things act in concert, but the players should be able to tell you exactly what their powers and abilities are and how the work.
If a player looks to you every time to explain what their options are, what their attacks are, how to calculate their attack roll, it shows that they don't really know their character well enough. In these case, eventually you must push back and make them figure it out on their own. Like spoiled children, if you do it for them every time, they will never do it on their own.
You do not have to be a jerk to accomplish this, though you will potentially have to call out players at the table.
For Example:
Guaranteed that after being skipped over a few times the unprepared player will write down their attack bonus!