Both landlord policy and umbrella policy.

Something that came up is that we bought an umbrella policy (specifically because of the rental), but I'm not sure how much of it is or isn't tax deductible (if anything).Part of the umbrella policy covers the rental.

Look at getting a good umbrella or general liability policy through your local broker so that you are covered and all will be well if anything ever does happen.

Also, do you think we need an umbrella policy with this?

Each property has a million dollar coverage and on personal there is a 4 times the umbrella in relation with net worth.

Recently it was suggested to me that a better alternative is to have a massive umbrella policy and not use an LLC.

Grouping properties for insurance/umbrella coverage can factor in.  

I am analyzing potential properties through the BP analytical tools and often feel I need a better umbrella overview of the Chicago market to then narrow down to witch neighborhoods I feel best investing in being a new investor.  

Personally I just keep things in my name with an umbrella insurance policy.

The cost of setting it is up is not really much but if you are looking at one house, then just get an umbrella policy and they should project you based what I have read so far.