I would like to share an experience with my Galaxy S6 after updating to 6.0 Marshmallow over OTA. Before, with Lollipop, I have used only swipe lock screen, although I have had my fingerprints configured properly (I did not now what fingerprints backup password was). After the update, I wanted to change the lock screen from Swipe to None. I could not be able to do it, because my phone was asking for my fingerprint or backup password. Any of my fingerprints did not work.
So after looking on this forum I have found a post from "njdan30", where he suggests: "go to google.com/android/devicemanager and sign in send signal to lock device with your password of choice and then your phone will ask u for that password then your in".
So I locked my device remotely through AndrDevMan and then my phone was locked by PIN. Then I was able to go in the lockscreen settings and also in the fingerprints menu again using just the PIN I did set in ADM.
From this point you can set up whatever security method you prefer. Hope, this post will help to someone. Cheers!