[Galaxy Note 10.1 Q&A, Help & Troubleshooting] obscuresword:
I don't have a Note 10.1 (my uncle does) but for me it all depends on what you want them to do on your particular device, and your needs. For instance, my galaxy player didn't manage memory well so I needed an app to do that.

Also if you want to see most of the root apps in the play store, just type in "root". You still have to do a bit of digging to see which ones suit you but at least it gives you a better start. Anyways my list is as follows:

SuperSU/Super User- This is a mandatory install because you need to give root apps super user permission to work with your system. It doesn't matter which one you pick, because they both work really well.

SuperSU- https://play.google.com/store/apps/...51bGwsMSwxLDEsImV1LmNoYWluZmlyZS5zdXBlcnN1Il0.

SuperUser - https://play.google.com/store/apps/...wsMSwxLDEsImNvbS5ub3NodWZvdS5hbmRyb2lkLnN1Il0.

/system/app mover - It can set/remove apps as a system app, meaning you can remove all the bloatware off a device or set apps of your choosing that can't be uninstalled from the launcher. https://play.google.com/store/apps/details?id=de.j4velin.systemappmover&hl=en

AdFree- Gets rid of Ads (no longer in the playstore)

Auto Memory Manager- As the name states it automatically frees up your ram in order to keep your device running smoothly. You can set thresholds, tell which apps to ignore, and etc to customize when you want it to start managing your ram. You don't have to have root, but it works much better with it.

https://play.google.com/store/apps/...wxLDEsImNvbS5saW0uYW5kcm9pZC5hdXRvbWVtbWFuIl0.

Clean Master- This app is almost a jack of all trades. Not only does it also manager your ram. It cleans out junk files that are unneeded, deletes private data (i.e web browers data), and can move to SD, Uninstaller, or Backup your apps. It is very easy to use. I think of it as the CCleaner for Android.

https://play.google.com/store/apps/...GwsMSwxLDEsImNvbS5jbGVhbm1hc3Rlci5tZ3VhcmQiXQ.

CPU Master Free- This is a cpu controller that can set your max, min, scaling, have profiles (if using pro), can control your i/o scheduler, and voltage. This pretty much means your can increase the performance of a device, or increase battery life. It's really nice for a free app. However, almost any cpu controller app does just fine. I heard SetCPU and Tegrak were the best.

https://play.google.com/store/apps/...sMSwxLDEsImNvbS5hbnR1dHUuQ3B1TWFzdGVyRnJlZSJd

DSPManager 1.0 (not in the playstore anymore either) - This app really helps out with the quality of music, and you can set profiles for headset, BT, and speaker

Root Uninstaller- This is one of the best and most essential root apps imo. This backs up apps as an actual apk file automatically. It also treats updates for apps as a separate file too. On top of that it can restore apps, reset apps to their original state, freeze apps, and etc.

https://play.google.com/store/apps/...sMSwxLDEsImNvbS5yb290dW5pbnN0YWxsZXIuZnJlZSJd

Titanium BackUp Free- If something doesn't work in root uninstaller I use this. It does everything that root uninstall does, and a bit more. The only thing is it doesn't back up apps as apk files. I still consider it to be a 5 star root app. Just make sure you have Busy Box installed.

Titanium BackUp Free- https://play.google.com/store/apps/...DEsImNvbS5rZXJhbWlkYXMuVGl0YW5pdW1CYWNrdXAiXQ..

Busy Box https://play.google.com/store/apps/...51bGwsMSwxLDEsImV1LmNoYWluZmlyZS5zdXBlcnN1Il0.

Have fun searching and looking for the apps that best suit you. :D