I got a standard CA homeowner's policy that is $126/mo with a $1,500 deductible.My Dad brought up that since I have tenants, I may need landlord's insurance that would protect me further.

Unless you have a tremendous amount of assets you're needing to protect, you're going to be wasting time and money setting up a LLC or similar. 

Also, the crisis was so severe, your Lines would have been automatically closed and you would have no access to that Line anymore.So I moved the money into the Stock Market / Bond.For the inevitable crash, I placed some in US Bonds and some in safe stocks with PUTs (hedges against a down fall) in place, protecting the money taken out from the lines.To make a long story short, I was in very good shape to pick up a new property because I had the cash available while a lot of investors did not.I could only have done that by utilizing the Stock Market.An Investment Vehicle with only Real Estate is hard to steer.

They will provide healthy insights into management concerns as well how to protect yourself best.

While in the process, I was advised to title it under an LLC (asset protection).

These folks you need to talk to - let them know when the rent is due and when it is late and review the terms of their lease.When leases expire you may want to use your own lease with clauses that will protect you.You should talk to your inherited tenants and do an inspection of their unit.

Take time to clean dirt, remove nails, spackle and sand, it doesn't take much time to do it right.Hopefully you haven't already done new flooring, if so be sure and protect it.

The down payment protects you when there is a market downturn. 

If you don't like the rules a tenants  best option is to leave.If she wants protection from lawsuits all she needs is adequate insurance, A LLC or trust does not provide any greater protection and is a unnecessary expense.

Do you have a complex tax situation or are you looking at a liability protection strategy?