First, let me congratulate you: you're having the problem that your players are having too much fun. As an inexperienced GM, this is the best problem you can possibly have, as long as you don't stress yourself about providing the material (don't be afraid to ask for more time).
However, the solution is easier than you seem to think: just tell them beforehand. There's no need to pretend that D&D isn't just a game; you know it and your players know it. You don't have to give away the plot just to say "Hey everyone, I'll be running a one-shot tonight." All they know is that the plot will be wrapped up by the end of the night (if things go well). There's no need to give them the false sense that their adventure might continue on if you have no desire to do so. Indeed, it's definitely worse to be disappointed that a story you liked suddenly ended than to know a story you haven't unravelled yet is going to end by tonight.
That said, please feel free to expand upon your one-shots. There's several different ways to DM, but I personally prefer to write what's happening next between sessions, not plan out the entire campaign in advance (although I will think of some good ideas on where to go next, I won't decide until later). If your players really liked one of your one-shots, there's no reason you can't make it into a real campaign, even if you never planned on it -- tons of campaigns happened this way. And you certainly don't need to write up your entire campaign as a module for it to be "valid" or even quite good.
Their characters are fine.
Optimization in 5e has very little to do with individual characters, and everything to do with the party as a whole.
Unless the players are highly organized, builds with high stats and dump stats would actually be a liability. I'll explain this by comparing it to Pathfinder:
In Pathfinder, each character takes on a specific role in which their competency, assuming the character is optimized, grows exponentially. For example, a wizard may invest a level or two into multiclassing rogue, and it's better than nothing, but they won't hold a candle to the "real thing." At some point DCs for skill checks and saving throws get so high that only a specialized character has a real chance.
In D&D 5e, a character specializes in a number of things, but this generally only means that they are a step or two above the rest. For example, say a wizard takes the criminal/spy background; for 99% of your adventuring career, that wizard can be relied on to handle duties that are traditional to rogues, though they will likely approach said duties in a different way. No multiclassing required.
This is because of the bounded accuracy thing. You always have a chance. Having a decent wisdom score on a barbarian isn't a waste. Hello, mind control!
Because of this, it's less important in 5e that you specialize. Instead you optimize by having your party, as a whole, make sure that all bases are covered. And redundancy is more likely to save your bacon than a slightly higher bonus to your already-high rolls.
5e adventure design assumes players to be sub-optimal
To some extent, whether individually or as a cohesive unit. So you don't really need to ease up on anything. In early stages you might want to give them some light warnings when they're about to enter a deadly encounter. A wake-up call so they realize, "Oh we should play it smart" is more than enough for most parties.
As far as what I mean by "balance": it seems that at levels 1-2 it's
hard to keep everyone conscious the whole time since they have so few
hit points; better to anticipate a KO or two and bring your healing.
This is not a consequence of the characters being built for breadth. It's a simple matter of how fast and deadly combat is in 5e. Perfectly normal for any party.
Some DMs will start tuning down encounters once players start dropping to zero health. Don't do this! They survived, they learned, they will be excited, they will be tuning their party up.
That's when you start targeting players' weaknesses. At which point, it's a good thing they went for breadth.
Total party wipeouts are not the end in Curse of Strahd.
Check out the Adventure's League Dungeon Master's Guide v4 that accompanies Curse of Strahd. Look under Jeny Greenteeth's spellcasting services, and the block on "Death in Ravenloft." This is a canon method for continuing the campaign in the event of everybody dying horrible deaths.
So by all means throw that coven Night Hags at a team of level 5s! They might surprise you and curbstomp the things. Or they might all die and come back with some Dark Gifts.
Challenge Rating is accurate but not precise.
You can read about it in the DMG. CR is based on Proficiency bonus, HP, AC, attack bonus, damage per round, and DC on their abilities. It is not adjusted for the special abilities they have, and how those can play with different parties.
For example, I've run Death House a few times. The Shambling Mound is CR 5. It's supposed to be tough, but parties have had little trouble with it. On the other hand, each party was seriously thinking they were going to die when I unleashed that pack of five CR 1/2 shadows on them.
The CR does not account for how a devious DM may capitalize on special abilities, or how a given party may completely shut an enemy down.
Best Answer
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?
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.
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).
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.