The following is based on the assumption that you are paid as an independent contractor and your earnings are reported on Form 1099-MISC. The purchase price of the car and, quite probably the initial repairs costs, if needed to make the car usable, would not be a current year expense. These costs would be the basis of a depreciable asset. If you are then going to use that asset at least 50% for business purposes, you could, in each future year, take a deduction for the business share of the actual operating costs (gas, oil, minor repairs, registration, insurance, etc.) plus the annual depreciation. Or you could make life simpler by taking the standard mileage rate for all your (carefully documented) business miles. For 2017, the standard mileage rate will be 53.5 cents per mile.
If you are a W-2 employee, you can still take a deduction for unreimbursed employee travel expenses, but these expenses are limited to those that exceed 2% of your Adjusted Gross Income, and are only deductible if your itemize deductions.