Advice on first rental property

My wife and I have owned our home for about 4 years and are going to be upgrading into a home better sized for our family.

We got in at a good time so we are planning to rent the property as we expect it to be able to cash flow.

I have always been a bit of a worrier so I am trying to plan how to limit my personal liability with Renting. I reached out to my original mortgage company and they told me they are fine with me moving the deed to an LLC but the mortgage will stay guaranteed by me personally.

I have a bit of anxiety about how it will work actually moving the deed. Is there any risk in doing that? Is the additional coverage worth it vs. just getting a more comprehensive insurance? What should I know or consider for this decision about whether to rent the property through my own name or by putting everything under an LLC.

My mortgage is around 1200 per month and we expect to be able to rent between 1750 and 1850.