This is not the case. There are 2 kinds of ROM's. One is cutting edge with the latest updates from Google source code (which can be filled with bugs and it takes the devs a little while to crack) and then there are ROM's based on previous source code that is stable.
For example, most ROM's on Android 4.1.1 are very stable and have either reached their end of development or are moving forward to 4.1.2 or 4.2.x for additional features. The base of that code is stable, but the additional features may cause issues. For example, adding the 4.2 Keyboard or camera to a 4.1.x ROM.
My wife owns a Note 2 and this ROM has been the most stable and reliable for her, and it is based off the Int'l version of the Note 2, so no AT&T or carrier crap is installed:
http://forum.xda-developers.com/showthread.php?t=2016575
Not sure what carrier you are on, but pretty sure this works on most North American carriers like Rogers, Telus, ATT, etc...
Before you root and rom, I highly recommend that you read everything you can about the subject on the XDA Forums. And I don't recommend using OSX to do anything with Android. It can be done, but when you are new to this, it is just easier to use Windows. (So if you don't have a Windows machine, then use Bootcamp on your Mac, partition out around 50gb and install Windows 7 (not 8!). Don't use VM Ware or similar "virtual" Windows on top of OSX. You need to boot your Mac into Windows.
Good luck.