Everyone has different circumstances and its definitely a personal preference. I have a storage unit. My house was built in the 1950s and the combined closet space is less than the master closet at my parents house. We have a low pitch roof and hardly any attic space. We don't have a garage. The first storage unit I moved stuff into had about 50 units broken into the morning of my move in, so I didn't stay for long. The one I am in now was brand new when I moved in and a bargain price, but now my rates have doubled in the two years since then. So, does it make financial sense? On the one hand, it cuts into my profits significantly. It is also a hassle to get everything in and out of storage, but I have worked out a pretty time efficient system that works for me. That said, if I did't have a storage unit, I just couldn't resell anymore. I have no other place to put inventory. I enjoy this side hustle and still make enough money that its worth it to me. It is not anywhere close to ideal and I can't wait until we either add on or move to a larger house, but if you need storage, you need storage.
As for safety, I would just do everything to avoid drawing attention to yourself. For me, everything goes in and out in a moving box. Don't set up anything so that someone can see that its LEGO in there if they walk by while your door is open. My goal is to spend as little time there as possible. And yes, get insurance from an outside source.