If anyone is downloading Kies from Samsung.com, note that there is a new version specifically for the Note 3:
For Windows: SAMSUNG KIES
It's a beta version, but it's what I used (and installed before I connected my N3 the first time), and haven't had any issues.
I do get prompted to install some Verizon utility that's supposed to "help connectivity", but I'm cancelling that every time I connect it to a Windows PC. I have more VZW software on the phone than i need/want, definitely don't want any VZW software on my PC.
Has anyone installed that software from Verizon? What is it?