Hi daryn-11
Congratulations on the purchase of the home and rental!
Both you and your father will report the rental income received on your Schedule E of your tax return. You will want to keep track of expenses paid separately, as you will each deduct the expenses you paid. You also will each report 50% of the depreciation of the property for the portion that is a rental.
Here is a great IRS resource, https://www.irs.gov/pub/irs-pdf/p527.pdf
If you create an LLC for the property, that would be a partnership since two members and would require a partnership tax return.
I hope this information is helpful!
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