I've finally gotten a TWRP version to work for the J320ZN with no issues. I've had a week of tinkering so I thought I'd go back to my phone and try on that again too after previously giving up.
To repeat what I've already written, the suggested TWRP version for J320FN DOES NOT seem to work. When manually booting to recovery after flashing, you get stuck on the default Samsung boot screen, but with Download Mode text still stuck in the corner (to finally answer your question ashyx)
I got TWRP J3lte to work. To download:
https://dl.twrp.me/j3lte/
I've had a BILLION problems doing this... because like the OP, I couldn't get root by using SuperSU.zip through TWRP.... it would cause a bootloop. I tried the suggested version of SuperSU posted by ashyx earlier in the thread... plus the latest with no luck.
My "solution" (LOL) was to flash CF-Auto-Root... without realizing it wiped to stock recovery! So here's me all happy thinking I've got TWRP and root...and gotten rid of the bootloop until I set up my phone and went to recovery to make my first full backup... and saw that not only was I getting stock (DUH lolol), but a dm-verity error.
This is something I know nothing about, other than there is a patch for it. So this time, I decided to try the dm-verity patch and REAL SUCCESS! Root, TWRP recovery (that's still there after multiple checks).
So... if you've tried TWRP j3lte and the latest SuperSU.zip and instead of working, you got bootloop you could try the dm-verity patch in your procedure (also to get rid of the bootloops I just flashed CF-Auto-Root again... but then you'll have to start again with TWRP etc).
My successful procedure was:
1) Install TWRP j3lte as linked above (lastest version twrp-3.2.1-0-j3lte.img)
2) Install SuperSU v.2.82 SR5 through TWRP....
https://download.chainfire.eu/1220/SuperSU/SR5-SuperSU-v2.82-SR5-20171001224502.zip
3) THEN BEFORE REBOOT, install Dm-verity and Forced Encryption Disabler patch (no-verity-opt-encrypt-6.0.zip) from
https://androidfilebox.com/miscellaneous/dm-verity-and-forced-encryption-disabler/ using the same "Install" button/method in TWRP.
Then you can reboot and THIS TIME it worked... I've rebooted many times, recovery still there, got root.... Link2SD working fine and I've made several backups to test.
A comedy of errors.....but I FINALLY fixed it just through tinkering. Hope this helps.