Better to buy property in LLC or my name with personal umbrella insurance?

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Hello,

I am trying to buy my first duplex in Florida and am close to closing. I am very concerned with personal liability in case someone gets hurt on the property.

It seems like I have two options for insurance:

1. Buy the property in a Florida LLC and get a dwelling insurance plan that will cover my personal liability up to 100k.

2. Buy the property in my name take out a large personal umbrella policy to protect my personal liability (likely 1mm in coverage).

Both policies are comparable in cost. Which do you think is better in order to protect my personal liability? I am concerned that if my LLC is sued, the attorney may try to "pierce the corporate veil" and come after my personal assets. Is the personal umbrella policy an adequate way to insure myself against liability risks?

Joe