The LG G3 is LG's newest flagship phone. However, based on which country you live in and what carrier you use, there are several different models of the phone. Overall, the hardware is the same, but where the differences arise are mainly in memory configuration and wireless charging. Otherwise, the CPU, GPU, the body, etc are the same.
This post only gives the information needed to root and unlock (aka bump) your phone. It does not outline how to flash to different stock images.
All models of the G3 at this time can be rooted, but that depends on what version of software is on your phone. Luckily, at this time, all Kit Kat versions of the LG G3 can be downgraded to a previous version. You don't have to be rooted or "unlocked" to do this. However, with Lollipop on the horizon (with many foreign countries already getting it on their G3s), that could change. Reports so far say people are still able to flash back to a previous version.
Go to the following link which provides a spreadsheet of information for each of the different models of phones and whether root is available or not:
https://docs.google....roMs/edit#gid=0
This will tell you the version that is rootable. If you are on a higher version than what allows rooting for your model, then you need to go here to learn how to flash back to a previous version and get the correct image files for your model of G3 before you root.
http://forum.xda-dev...d.php?t=2785089
Once you have determined which root exploit works for your phones model and software version, follow the instructions for that root exploit and you will be rooted.
Once rooted, you can then flash TWRP via Flashify which has been "bumped" to allow flashing custom ROMs and kernels. Remember, you must be rooted before you can flash TWRP.
Get TWRP here:
http://downloads.cod...bed/lg_g3/bump/
Get Flashify app here:
https://play.google.....flashify&hl=en
Once you have flashed TWRP, you can then flash custom ROMs and kernels.
NOTE: When flashing custom ROMs and/or kernels, you must ensure you are using a bumped ROM or kernel specific to your model of phone. In other words, do not attempt to flash a ROM/kernel for the AT&T G3 (DS855) onto your Verizon G3 (VS985). You will brick your phone and it will be a pain to fix it. If you do not heed this advice and do this, do not ask for assistance in this forum. You have been warned!
You can find plenty of ROMs and information from the following links:
Verizon G3 (VS985):
http://forum.xda-dev...oid-development
http://forum.xda-dev...rig-development
All other G3 variants:
http://forum.xda-dev...-g3/development
http://forum.xda-dev...rig-development