For me, I had the UAG Maverick case since the I bought the device. The UAG adds some extra width to the phone which I did not care for. I have bought 2 cases from Amazon. One is an Iroo and the other I cannot remember the name. They both are slim cases and do not offer the same degree of protection as the UAG but, it makes the phone more manageable. For example, I could not use many of the cell phone car mounts with the UAG because of the width. With the other cases, I can.
The one thing that I do not like about the Note Edge is the lack of glass screen protectors. I tried the Verizon one and that was on for about a week. I also tried the Skinomi and that was easy to apply. But, it does not look very good right now. So, i am thinking of going without one. I used to not have one on my Iphone 4 and had a couple of scratches on it after a couple of years.