In most places property taxes that you pay are based on the appraised value of the home or property when the tax assessor comes by and appraises your property.
Although when you do buy a home and the deed changes from the seller to you then your taxes might be based on the purchase price of the home for at least the first few years.
The way property taxes are based can depend on your county and location but most times your property taxes will be based on the appraised value set by the tax appraiser when they visit your home.