Prerequisites include a minimum of a 4.3 bootloader and modem. If you are not on the official 4.4.2 bootloaders and modem then you will need to flash ktoonsez kernel. http://forum.xda-developers.com/show....php?t=1756776
Before you do anything you may wish to consider, if your phone is not carrier unlocked, using the free method to take care of this: How to unlock your I747 (AT&T Galaxy S3)firmware 4.1.2 (FIRMWARE DOWNGRADE INVOLVED!) You would not be downgrading since you are on 4.1.1. This unlock could never hurt, and survives upgrades.
If you are wanting to update to KitKat it will take several steps to get there. As @canodroid15 suggested you will need to go incrementally. The simplest way may well be as chitown835 recommends, unrooting and then taking each OTA in turn. I'm not sure, but you may also find you need to return to a stock recovery to receive the OTA updates. This will step you from 4.1.1 to 4.1.2 to 4.3, at which time you could then flash then ROM followed by the ktoonsez kernel. Or you simply take the next OTA to 4.4.2. Generally you are forced to wait a day between each OTA. This waiting period can be shortcutted by changing your system time/date after each OTA.
If you do not wish to unroot or remove TWRP to go through each OTA you will still need to update the bootloader and modem incrementally. Use caution, the bootloaders and modems are not the same for the i747 (AT&T) and the i747M (Canadian and Mexican variants). IF you are on the i747 go through each step. If you are on the i747M I would suggest doing the same, though it may not be required until you reach 4.3. To reduce chances of problems update the bootloader and modem together, keep them at the same version. Once you are at 4.3 you could do as you asked: flash the ROM and then the kernel.
Check the first post of the thread. It states that you must be on at least the 4.3 (MJB on the i747, or MK5 for the i747M) before flashing this zip. If this is the route you take, be sure you do not get the stock image dump from the first post, it includes the bootloader and modem, your day would be ruined if you are on the i747M.
I'm trying this upgrade on my T-mobile T999 (galaxy s3). I have a few rookie questions that hopefully can be answered. I assume I cannot use Odin to do the flash/upgrade and I have to boot into recovery mode to complete this upgrade.
Can I make 3 new folders (rom, kernel, modem) that contains the *.zip files in them on the SD card and try to install each one by one, in that order? Is this how I should do it?
Thanks for any help in advance.