Ladies and gentlemen, I have a confession to make--I believe that I am very much a heathen when it comes to proper storage.
My batteries follow me where I go. When I am in front of the computer, there is one somewhere to my left and one somewhere to my right. I will fill up a couple of tanks, vape for a few minutes, and switch to another tank. If the batteries are on the charger or taking a rest, the half-filled tanks will sit in random places, waiting for me to make a move. There have been a few times where I could not remember which juice was in a particular tank. Mmm, tastes like molasses--no, wait, maybe it's maple, but what the hell is this called again? Nor could I remember when I last switched the coil. By the way, I find that it is best to do when switching to another powerful flavor. Although I often just wash the tank and coil in warm water and let it dry overnight.
I carry my battery in my shirt pocket sans anything protective. I constantly check to make sure it is still there (unless it's clenched between my teeth), but if I'm not wearing a shirt with a front pocket, I will keep it in my coat or pants pocket. So far, nothing has leaked onto my clothes, but I'm not above using the corner of my undershirt if the tank floods the battery a bit. That would perhaps be drastic, but like I said, I'm a heathen and don't often carry around napkins or protection. Wait, nevermind...
Either way, don't do what I do. I do take care of my equipment (by cleaning the batteries, tanks, and coils), but old and bad habits are hard to break. After all, most of us are former smokers.