I picked up this case and abso-friggin-lutely love it. The phone's so slim, and this case doesn't bulk it up... I had two people ask me if I was going to get a case for my phone... then I told them it was ALREADY in a case!

http://www.amazon.com/gp/product/B00F423NQ2/ref=oh_details_o01_s00_i00?ie=UTF8&psc=1

I also picked up this car mount that I love. It's not specific to the Note 3 but is much nicer than most universal mounts I've found and the company also provides a car-dock app that amazingly ISN'T garbage! This car mount works whether your phone is in a case or not but isn't nearly as bulky as a lot of universal mounts.

http://www.amazon.com/gp/product/B00AOCSFYC/ref=oh_details_o02_s00_i01?ie=UTF8&psc=1

I use AutoGuard BlackBox as a dashcam app with this mount and the iBolt Dock'n Drive dock mode. It works great. I have the Dock'n Drive turn on Bluetooth only when I mount the car in the dock and it turns it off when I remove it from the dock as well. It's all around a very nice setup.