the kernel choice you use to root is your preference, i use CFROOT, because chainfire is a tried and tested longtime reliable developer, is apps are usually solid, i was on the galaxy note and chainfires work was always the best.
Always backup the efs to the pc and keep it safe, no real reason other than you then have a backup to restore just in case your usb storage or sd card gets accidentally damaged or wiped, its always wise to have an extra copy of a backup.
i also use cfroot because it includes a version of clockworkmode recovery and the cwm app, using the cwm app you are then able to flash custom roms from recovery, stock roms from the app or even kernels, without ever having to use the pc odin again and everytime you flash a new stock rom through cwm app you keep the root, so no messing afterwards and no horrible triangles or counter increase,. its just the job.
So in order of prefernece, this is how i install and gain root, from scratch.
1 - install my stock rom through odin.
2 - i then use Initial cfroot flasher to flash the zimage of the kernel and gain root.
3 - i then install mobile odin which i purchased because its also a good flashing tool for the phone and of course i already have the cwm app from step 2.
in the future
If i want to flash customisations or mods, themes, custom roms, i use cwm app to boot to recovery mode and flash them from the sd card.
if i ever want to flash another stock rom, the procedure is this -
1 - create a folder in the root of your sd card called firmware.
2 - copy the unzipped file(s) from the downloaded stock rom to the folder you made, and also the matching cfroot kernel for that rom.
3 - Then run cwm app, select Flash Stock Firmware, itll ask a couple of questions and ask about root, select the cfroot kernel you copied to the card as the source for root, not to keep the stock kernel, or youll lose the root.
4 - it then reboots to flashing mode and does what it needs to do, it will again reboot and appl the multi-csc etc.
After this it will reboot to the firmware where you are now on new rom and rooted, bingo.
IF YOU GET A HANG OR BOOTLOOP
dont panic, just pull battery, put battery back in, hold the 3 buttons down to boot to recovery and do a full wipe, then restart the system, job done.
Ok people do you different kernels and methods of flashing, but seriously this is why i flash the way i do, purely so i dont have to piss around with triangle away or jigs to reset counters, all that can be avoided and anyone who flashes a custom kernel through pc odin is just being lazy, there really isnt any need to do that, you can gain root by other methods like the ones ive already mentioned, even mobile odin lets you root your phone when flashing a new rom.
It sounds like you have the system sorted now and running anyway, if its working for you with that kernel then just stick as you are, happy days, i just always stick with cfroot for the reasons ive mentioned.
Anyway glad youve got sorted now, hopefully no more problems.