LLC, but self-managing the property--liability

[Bienes Raices]

I want to buy a property using an LLC, to rent out. I will be managing the property myself. As I understand it, I can still be sued personally in some cases if I'm managing the property myself, even though it's held inside an entity. Is it best to co-insure the property in both my name and the LLC's, so that if I'm sued personally I'm still covered? Is there some other insurance setup I should be considering? As I understand it, my personal umbrella policy will not help in this situation. Thanks.