One of the great things about the Chrome Web Store is that like other "app" stores, there are frequently multiple choices for apps that fill a given need. Since nearly all of the apps are free, it doesn't hurt to try different things until you find a good fit. In most cases I've found things that work at least "well-enough", in a few cases I've found things that are fantastic, and in rare cases I've simply found the current choices just aren't very good (yet).
I have a Toshiba Chromebook 2, which happens to have a nice trackpad - large, smooth, accurate. However there are just times when I prefer to use a mouse. The Chromebook supports just about any standard mouse, whether connected by USB, Bluetooth, or receiver. My choice is the Logitech M325. It's small enough to carry around, big enough to actually use, and battery life is very good. The M325 uses the Logitech Unifying Receiver, a tiny USB wart that doesn't stick out very far (I leave mine plugged in all the time, whether or not I'm using the mouse). No extra software is required to use the mouse, but if you want to link more than one Logitech device to the receiver, there is now a "Logitech Unifying For Chrome" app you can install from the Web Store which will allow up to six devices to use a single receiver.
By default, you can "print to PDF" and have the file saved locally or on your Google Drive. If you want an actual hard copy printout straight from the Chromebook (i.e. without having to transfer the file to another computer to then print), you will want a Google Cloud Printer. Quite a few printers these days are Cloud Print-ready, meaning they do not need to be shared from a regular PC or Mac. My choice was the Brother HL-L2380DW, a black and white laser printer with copy and scan features.
The Chromebook will (usually) have either 16 or 32 GB of local, SSD storage (actual available storage will be less due to spaced used for the OS). Although the design goal of Chromebooks is for you to use cloud storage for most of your files, there are times when it's useful to have some things stored locally - for example if I'm going on a trip and I'm not sure I'll have solid Internet connectivity, I might want to load up some movies to take along, etc. Pretty much every Chromebook has an SD card reader. They also have one or more USB ports, so various types of USB drives can be connected (from thumb drives to hard drives, etc.). My choice was to buy a 64GB microSD card and to leave it in the machine at all times. It was pretty cheap, it's fast, and at least on the Toshiba it mounts flush.
Google offers new Chromebook users 100GB of Google Drive storage free for two years. Then if you wish to continue using it you can pay a monthly or yearly fee for whatever amount you need. By that time you should have a fair idea how much you actually need, which may be far less than the 100GB. As fond as I am of Google, I hadn't used by Google Drive much prior to owning the Chromebook. Now that I have one, I have added Google Drive access to my desktop Mac at home, and my desktop PC at work, and it's so easy to move things around that I am wondering why I didn't do it sooner. It's SO much easier than copying files to thumb drives, emailing them around, etc.
Chatting (Instant Messaging)
Right now all I'm using is Google Hangouts on the Chromebook. I don't do much Facebook messaging but I can do that within the standard Facebook web interface just fine (if I ever install a Facebook messaging app that I like, I'll add it to the list). I have not yet tried any of the options for linking to my phone for SMS messaging.
I use Google's Docs & Sheets. If I needed to do a presentation I'd use Slides. I do not work on "work" documents on my Chromebook, it's only my personal stuff, and for that the Google choices are more than adequate.
I have been using Sunrise Calendar for a while now and I really like it. It interfaces with LOTs of different calendar systems and merges everything into a single, useful view. I like that it pulls in Facebook birthdays and events. I also like that it runs in a separate "app window" on the Chromebook. I almost always have Sunrise open on my Chromebook.
Note - I'm not a heavy Reddit user, certainly not an expert on it. I have installed Reditr, a neat Reddit reader that runs in it's own app window and has nice multicolumn display, similar to Tweetdeck.
Obviously I just browse to Facebook like normal, but I have installed Social Fixer For Facebook which cleans up a lot of the clutter, makes it easy to preview images, etc.
I mainly use my phone to browse Instagram activity, but when I want to do it on the Chromebook I use Pixta. It has a clean interface, allows you to comment, "like" images, and download them for offline use.
I used to use Evernote, but I was never a power user. When Google introduced Google Keep, I ditched Evernote. Since Keep synchronizes with the Google Cloud, and since there is a nice interface for it on my Android phone, I'm a happy guy.
This is a crowded category, and I'm not entirely sure I'm done trying to figure out what I ultimately want. For years I loaded my personal music on my phone's SD card, and for those times that I wanted streaming music I used Slacker. But for about a year I have been using Google Play Music, and yes, I am subscribing to the paid version. I have uploaded almost 3000 of my own files, so I can listen to my stuff any time I have an Internet connection. Google Play also has lots of curated "radio stations" which are tied to various moods and genres, and I like that I sometimes find new stuff (or get reminded of old stuff) that I like. It's not perfect, but it's filling the need. I also sometimes listen to TuneIn Radio, when I want to listen to actual radio stations. There is no good app on the Web Store for TuneIn at this time. Also, some types of streams are not currently supported on the Chromebook, so your mileage may vary.
That's it for now. I'll be updating and adding to this list as I go. Feel free to comment, and make some suggestions. I certainly don't mind trying new things!