If I buy ghosts for the Xbox One, put my Call of Duty account on it and keep my 360 version, will my stats transfer over or do I HAVE to upgrade my 360 version?
YYou will be able to go back and forth and your progress will keep. We have done the cod app and have tested this going back and forth from the 360 to the 1 several times and no progress is lost .
It is as OUHATEME said, you can switch between xbox consoles and keep your progress. However, if you have DLC such as the season pass on your 360 version, you will need to digitally upgrade in order to have that DLC transfer over, otherwise you're going to have to buy another season pass. More info here Call of Duty®: Ghosts Seamless Next Gen Upgrade Plans.