Note that you have a choice of EITHER claiming mileage OR claiming actual expenses. You determine how your vehicle will be treated the first year you file. Mileage is generally the best way to go if you keep a vehicle for more than a few years, though if you lease a vehicle you should read through the IRS material to see which makes more sense for you. As a shopper some of my gas is 'free' as reimbursements on shops (and so I can't also claim it as a vehicle expense) and all of my oil changes are paid for by reimbursements.
If you claim mileage you can ALSO claim tolls and paid parking incurred for your business. Otherwise yes, you will need to determine what mileage was personal and what was business miles. If you have another job you will also need to figure 'commuting' miles to that work. I only have 'personal' and 'business'. I record my mileage Jan 1 every year and the difference from the previous year is total mileage. I subtract out my documented 'business' miles and everything else is 'personal'.