There is a tutorial on w0lfdroid that nicely explains how to use towelroot with newer kernel versions. This took me a while to figure out: the versions (NF2, NF3, etc) are the last 3 characters of your baseband version. So check which version you have under device info, mine was I9515XXU1ANI3, meaning you have to flash back the NI3 version. I don't know what happens if you don't flash back the right version. First you flash the ROOT version, that breaks your wifi. Load the root .tar.md5 archive in odin under AP, make sure you don't Re-Partition. Turn off phone and start download mode: vol down+home+power, then confirm with vol up.
Then, when running towelroot, you have to change the modstring, this is all explained in the tutorial. After rooting I installed SuperSU which automatically offers to get rid of all KNOX crap, and then
Then you flash back the NF3 version in my case which restores wifi.
Find the tutorial here www w0lfdroid com/2014/09/TowelRoot-Samsung-Galaxy-S4-S5-and-Note3-Android-4.4.2-NF-or-Later.html
For ultimate hand-holding, watch step by step video: www youtube com/watch?v=VqxSvsUMYco
Replace spaces in url with '.'s, I'm not allowed to post links but I hope this is ok.
This way doesn't trip the knox 0x1 flag, after this ordeal my knox is still 0x0. Some issues with spontaneous rebooting have been reported after rooting, I don't know if that applies to this method. Chances are you have to disable all knox apps which seems to fix this. I'm rooted for a full 5 minutes so no problems either way so far, I've just allowed SuperSU to disable knox.
I don't know about any custom roms or recoveries, main reason for me to root my phone is to remove all bloatware and be able to manage permissions.
I hope this helps anyone