I just wrap mine with a rag when I store it, on its side.
Since I don't use mind often, when I go to use it the next time I get liquified grease dripping down from the plunger--I hate that. And more oozes out from the bottom as you squeeze the lever. I'm still on the original tube that came with the gun; maybe it's the cheap grease that's creating the spillage.....or is it an inherent problem for all grease guns?
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I hang mine on a vinyl coated hook, on the wall. It's been working fine for 8 yrs.
I believe the plunger should be pushed back into the gun after a tube is loaded.
Here is what i did, I took a 5 gal pail, i took several sections of PVC pipe (2 & 3 inch) about the same depth as the pail. And glued them together all facing up. So i Have a couple of grease guns (1 air,1 pump) I also have several funnels. The grease guns hang from the open 3 inch PVC, in the pail and are up from the bottom of the pail. I keep newspaper in the bottom and change it when I remember. No pictures, I am at work.
Hang mine over the side of one of the many plastic drums we have in shop.
There is one near the work table that we hang all 3 over. That way if any grease comes out it goes in the can instead of one the floor.