It's unclear from the way you phrased the question, if this was your marital home as well (that happened to only be titled in your spouse's name), or if the court awarded you a property that was never your home. If this was your home that you lived in together, then you are overthinking the problem.
If you lived in the home as your main home before the divorce, and it was awarded to you as part of a property settlement as a result of the divorce, then you would report this as "Sale of your home" in Turbotax. The date acquired would be the date your spouse purchased the home. Your cost basis would be what your spouse paid for the home, plus whatever you and your spouse might have paid for permanent improvements. You are probably eligible to exclude the first $250,000 of capital gains from taxation. (see the special rules for divorced taxpayers on page 4 of publication 523 https://www.irs.gov/pub/irs-pdf/p523.pdf )
Mortgage interest and property taxes that you paid are deductible as a schedule A itemized deductions (how much tax benefit you receive depends on your other tax facts). Utilities, insurance and repairs are never deductible on your personal home. Improvements add to the cost basis and reduce your capital gains.
Treating this as the sale of a second home, or as an investment property, would only (maybe) be correct if you never lived in the home as your main home and the court awarded you a random house your ex owned instead of cash, as part of the property settlement.
