Thank you very much for the detailed tutorial. I'll just list a few things that I encountered during the process, if it helps anyone.
1) during TWRP flash, the 'flash recovery' command did not do anything the first time (completed, but recovery did not change). I tried the same command again, and this time it worked.
2) after flashing superSU.zip and rebooting, SuperSU did not show up. I installed it from the play store, and it worked.
3)Installed the SELinuxModChanger.apk, and tried changing to permissive. Even though SuperSU granted root access, the app failed to gain root privileges. Changed the 'force user' option in SuperSU for the app to ROOT, and it worked.
4)ES explorer couldn't gain root access no matter what I changed. ("sorry, test failed"). This happens because ES checks for 'su' files in /system/xbin, and our root method is systemless.
To fix it, I copied all files from /su/bin to /system/xbin and set permissions (using another root explorer, like fx or solid trial).
5)I had an older version of titanium backup, which couldn't gain root access. Updated to new version, and it worked. Backup and Restore works now.
It was easy finding solutions for these problems. You just need a search engine