Nice tablet! I have the Note 12.2 and love it. Posting from it as it's always on my desk next to me as I work.
There's the sticky thread at top for general Android apps.
However, specific to your 12" tablet there are a few. (Most of my essential apps for my Note don't apply because they are s-pen specific.)
I'd highly recommend a tablet-specific third party keyboard like Thumb Keyboard or Swiftkey. The stock Samsung keyboard isn't bad, but personally I like more options, especially on a.screen this size. For me,.thumb is my goto.
Dropbox. Check if Samsung still offers 50GB free as a bonus for buying a Pro tablet. (As well as 50 bux in app store cred)
If you're not crazy about the stock launcher, try Nova, or any others that are good for tablets as well as phones.
Button Savior (root or non-root depending). I find a 12" tablet so big that relying on the hardware buttons often is awkward. B.S. allows.you to have slide out software buttons at your fingertips.
Switchr. Along the same lines,.this awesome app allows you to switch tasks without relying on the hardware buttons. The combo of both of these is tailor made for a large tablet.
X-Plore (file.manager). On a large screen it's my favorite. Can copy between all sources, local and most cloud accounts. ES File Explorer is great too.
Camscanner Pro. I don't use the main camera for much, but this app makes the tablet a nice document scanner.
Jorte. My goto calendar/tasks app. I use a full homescreen page for a full sized 30 day widget which is great on such a large screen. acalendar+ tasks is also a favorite.
Quickpic- to replace stock gallery. Faster and better interface.
Moonreader Pro for reading books. On the 12.2 I prefer two facing pages in landscape mode... MR handles this perfectly.
ComicRack for comics. Comics are exactly 1:1 on a 12.2 screen. No zooming needed in portrait.. you can literally lay a comic book over the screen and its the same size. A better comic book reader you won't find screen wise. Weight wise holding the screen in portrait... that's another story!
ConvertIt unit converter. (Great tablet interface).
RealCalc
Hword (hopefully full version suite comes with your tablet. Closest to MS office on Android that I've used.
SideSync 3.0 -if you have a Samsung phone also, then you can use it directly through your tablet.
PocketCloud- control VNC servers. Again, big screen makes this highly useful.
The usual media apps: MX Player, Poweramp, Netflix, YouTube, etc etc.
Get tablified Market app to find apps you need with a tablet-optomized interface. (Unfortunately not a lot are. Biggest annoyance I run into are apps that will only run in portrait expecting a phone, when I run most everything in Landscape. Instagram for example is a hot mess on the 12.2).
Luckily, many apps are Multi-Window friendly. MW is no biggie on realatively smaller devices but its freaking spectacular on the 12.2. I'm always running apps side by side- it's created new ways of working that I litterally couldn't do with any other device. (For.example, I edit a ton of footage... I use my 12.2 to have a copy of the storyboard PDF, script, and rough cut of a show, and a note taking app running side by side on my tablet. The screen is big enough each task can be seen and used easily. Others are shuffling messy hard copy around while I can do everything with a single screen/device. (All of this offsetting the actual.work being done on a full workstation of course. )
Anyway, all the apps I can think of at the moment. Enjoy your Tab 12.2!