You would enter your Rental Property info under 'Property Profile' and also 'Assets/Depreciation'.
You are asked for the Cost (which is what you paid, plus sales expenses, plus any capital improvements made prior to renting), plus date 'available for rent', whether actually rented or not.
Any Capital Improvements made later, such as a new roof, room addition, for instance, can be entered as separate assets and depreciated also. TurboTax calculates all the necessary depreciation for you and gives you assistance entering items for Depreciation, and what Depreciation options you can choose. Some options are available for the 'first year of service' only.
County Taxes that are on your HUD Settlement Statement can be added to the Cost Basis as a Sales Expense. Later, property taxes will be considered a Rental Expense.
Renter's insurance can be an expense, as you don't normally depreciate 'contents', other than major appliances, or new carpeting, for example, which are entered as Assets.
Here's a few articles you may find helpful:
https://ttlc.intuit.com/replies/5161635
https://ttlc.intuit.com/replies/5361755
https://ttlc.intuit.com/replies/4209856
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