If you paid 60k for the property, and the tax assessment says for example the value is 100k, and breaks it down by 40k for the improvements and 60k for the land, then your basis for depreciation would be 40% of your 60k which is 24,000 depreciated over 27.5 years (note unless your sales contract specified the basis of the sales price allocated to each). But, also don't forget to add into your basis things such as legal and recording fees associated with the purchase, abstract fees, survey charges, owner's title insurance, and some other items (see IRS pub 527 or 946). On the other hand, points and origination fees, cost of credit report for loan, fee for appraisal required by lender, and a few other things are NOT allowed to be included in the basis that you depreciate.
The general rule is that anything that you do to keep the rental functional and things running is maintenance that can be deducted in full that year, and things you do that add value (such as replacing HVAC versus just paying for it to be repaired) have to be depreciated over the appropriate IRS schedule. This can vary from 5 years (i.e. computers, office machinary, some automobiles, appliances such as stove and refrig, and furniture used in the rental and carpet), 7 years (office furniture, office equipment, etc), 15 years (roads, shrubbery), and 27.5 years for new roof etc (time begins when work is done not when property was placed in service). Pretty much anything you do to keep the place and systems functioning is maint but when you actually replace something broken rather than fix it, you have to depreciate as capital expense.
