[Android General] Droidriven:
Go to this link and download the TWRP .tar file. You want the .img.tar, not the md5 or the .asc file. Store it on PC in a folder of your choice where you can easily find it.

https://dl.twrp.me/d2vzw/twrp-3.2.1-0-d2vzw.img.tar.html

Then download SuperSU.zip from this link and store it in the root directory of external sdcard in the device, get one if you don't have one.

https://download.chainfire.eu/696/SuperSU/

Then download the full set of USB drivers for Samsung phones, install the drivers then restart PC.

https://developer.samsung.com/galaxy/others/android-usb-driver-for-windows

Then download Odin 3.10 for Windows and install it.

https://xdaforums.com/showthread.php?t=2711451

On the device, go to system settings>about>build number, tap the build number 7-10 times quickly, when you see the message, go back and choose the developer options, find and enable USB debugging. Then charge the device to full, when fully charged, from the powered off state, press and hold volume DOWN+home+power, when you see warning screen, press the button to enter download mode.

Then open Odin on PC, with device in download mode, connect the device to PC, you should see a blue or yellow box that says COMM#, that means you're connected.

Then, in the options tab, make sure that the "auto reboot" option is UNCHECKED. Then click the AP button, browse to where you stored the TWRP .tar file, select it, when back at the Odin screen, click START. Let it flash, when it's finished, you'll get a green PASS.

After the PASS, disconnect the device from PC, remove the battery, wait 5 seconds, replace the battery and cover. Then press and hold volume UP+home+power, when you see the Samsung screen and the little blue text appear and disappear in the top left of the screen, let go of the power button but keep holding volume UP+home. It should boot into TWRP recovery.

In TWRP, select the "Install" option, select "install zip", browse the files to find your external sdcard and the SuperSU.zip file, install SuperSU. When it finishes flashing the file, go back to home in TWRP, select the "Wipe" option, then select "advanced wipes", only put a check beside the cache partition and the dalvik cache partition, do not check anything else, swipe the slider at the bottom to execute the wipe, after wipe finishes, go back to home in TWRP, select reboot then reboot system, if it asks about installing SuperSU to /xbin, tell it no and continue with rebooting.

When it boots into the phone normally, open the SuperSU app in your app drawer, it will tell you to update the binaries, update them, when it prompts to reboot, select "normal".

When the device reboots, it will be fully rooted, go to Playstore and update the SuperSU app.

Now you're ready to choose a ROM, I suggest something in the 5.0-6.0 range, anything newer will be too demanding on the old hardware in this S3. Anything 5.0-6.0 for d2vzw will work fine. It's been a while since I've used this device so I'm not up to speed on which ROMs are still available, you'll just have to look thru Verizon S3 development forums here, they'll be plenty of threads for d2vzw ROMs, only use d2vzw ROMs, don't use anything that says anything else. Something like OctOS for d2vzw or CyanogenMod(CM) for d2vzw.

Don't use anything that is made from any of the stock stuff from the Verizon S3, the S968C can't use any of the actual stock stuff from the Verizon S3, we can only use the d2vzw custom ROMs, TWRP recoveries and d2vzw Kernels, you won't need to worry with kernels though.

When you have found the ROM that you want to flash, download it and the gapps file that they recommend in the thread where you get the ROM, the version of gapps should match the android version of the ROM(i.e. 5.0-5.0, 5.1-5.1, 6.0-6.0, 6.1-6.1, etc..). Store them both in the root of external sdcard where you put the SuperSU.zip file.

When you have chosen the ROM you think you want and you've gotten the files downloaded and stored on external, let me know and I'll walk you thru the next steps to flash the ROM.