WOW dude. You have not rooted any Android device for four years? Damn man, that sucks! It's like not letting a bird to fly at sky and make her stuck inside a cage! Samsung's rooting process being the easiest too! It will take just 30 seconds to root your Note 2 dude. All you need is the latest version of Odin (I believe the latest being 3.09), which is a small software and then just flash Chainfire's auto root kernel kit (it's basically nothing but a stock kernel with busybox and init.d support), that's it, done.
Changing launcher won't do anything at all by the way, I mean anything related to battery that is. But still Nova or Apex are the preferred launchers over TW anytime. Use BBS as I/ some others have said, and monitor the wakelocks first.
PS : For some reasons I am quite confident that you won't head over to XDA and root it ultimately, so I am wasting a few seconds and attaching the necessary links myself,
CF Auto Root topic : [GT-N710x][SHV-E250*] CF-Auto-Root | Samsung Galaxy Note II GT-N7100, N7105 | XDA Forums [
Make sure you download the correct version depending on your phone's model, N7100 or N7105]
You can use the Odin which is linked in that topic (ver 1.85) or use the latest version, entirely up to you, both will work absolutely same. If you like latest version of Odin then download from here, Download Odin 3.09 - Odin download with Samsung ROM Flashing Tool [Hmm, I see the latest version is 3.10, I stand corrected]
Make sure you have the USB drivers installed on the PC for your Note II. Turn off phone, then press and hold Volume Down and Power button simultaneously, you will see a screen which will say press Volume Up to continue, do that, connect the USB cable to PC, some drivers will be installed if you haven't installed them on a previous occasion, this is important, so let them install. Then open Odin, you will see your device connected under ID : COM option in Odin, it can say COM1, COM2 etc., depending on which USB port you are using on your PC. Then hit on the PDA (for old Odin) section, or AP (for newer versions of Odin) and select that CF Auto Root package you have already downloaded. Select the .tar.md5 file, not the zip file, LOL. Hit on Start. Wait for 15 seconds or so.
Then later you might need to install Super SU's latest zip package, or maybe not, I don't own a Samsung any more, so can't say, but you need to have latest binaries installed. You can always get the latest package from here, SuperSU Download But to install that you must have a custom recovery installed, like TWRP or Philz etc. Stock recovery won't do, and you will have stock recovery unless you choose to install a custom recovery, keep that in mind.
Oh, You are welcome.