I don't think you have to hide the numbers for what you are doing, but rather just how you get them.
I've made my game more player facing, i.e. they players roll all of the dice. But I've also made it more narratively driven, i.e. the players don't invoke their powers, instead, they describe their actions. (Taken liberally from *World games)
I did this in response to exactly the problem that you're having- that DFRPG can be overwhelming at times. So how does this work?
The first part about the GM not rolling takes a lot off of the GM's shoulders, and makes things faster. You then use this savings to spend the time to interpret the players' actions, and trigger them based on the narrative for the players that are less familiar with the rules. Rotes help a lot with this.
So, the only things you have to explain to your player are- the rotes that you help them design with their characters, and the meaning of overcasting vs standard casting. Once you've done that, the player describes what they are doing, i.e. casting their rote, or putting more effort into it or really pushing themselves. You look at the numbers behind the scene, and give them the target. They roll... and describe what they are doing to invoke their aspects as needed, since they know what they need to make the roll.
This way, they are eased into the aspects of the game that have to do with Fate, while the crunchy things of magical manipulation are kept behind the scenes.
In summary, let them describe it in the narrative, you do the heavy lifting, then let them roll against a static number, invoking aspects as needed to make the roll if they want to so with more narration.
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
For the new players I highly recommend using the character sheets provided by the game publisher.
The benefits they provide are:
That being said, most of the experienced players I have played with preferred to just go with some graphing paper and arrange the information the way they want. The benefits of your own sheet are:
In the end it boils down to experience and personal preferences so never feel pressured or pressure other to go with one style because it's the player who will use the sheet 95% of time.