LLCs vs. Umbrella Insurance for first rental

[Joseph Gambino]

From everything that I've read so far on BP and abroad it seems like there is a questionable argument for LLCs vs Umbrella Insurance. 

So, let me start by saying I have my first rental property and am looking for the most effective way to cover my tail should the need arise. 

From what I understand so far and have picked up on both is that for an LLC if someone were to sue you that would protect your personal assets and investments and the only items that could be in danger is what is under the LLC. On the other hand, Umbrella Insurance fills the gaps for home owners insurance, auto insurance, and protects your personal value. The Umbrella Insurance would be the first to be eaten up before any of your assets or investments could be harmed. Am I wrong or is that the gist of it?

First time investment what would you recommend? Pros and Cons for an LLC? Pros and Cons for Umbrella Insurance? Or would you get both? Would Umbrella Insurance be applicable over an LLC? Many more questions but I'll let these start the discussion.

Thanks in advance to all that supply their input.