When the LLC promoters talk about asset protect, they usually set the scenario where your LLC is sued and your personally owned assets are shielded from exposure by the "asset protection" afforded by the LLC.
What they don't tell you is that when you self manage your own properties, either as the manager of a single member LLC or as a sole proprietor, then nearly any lawsuit arising out of your rental activity will be over something that you did as the property manager/owner, or something you should have done but didn't.
Since you personally manage the property, you are also personally liable for your actions. Does not matter that you were acting on behalf of the LLC.
That is why I say a single member LLC for rental property that you will manage yourself provides no asset protection.
Make sure you thoroughly discuss this point with your attorney.
For the property you self manage, just make sure you have adequate liability insurance. I can purchase liability coverage on my hazard insurance policy for an additional $25. A lot cheaper than the cost of establishing and maintaining an LLC, especially when most tenant lawsuits are settled within the limits of the insurance policy coverage anyway.