Tulum is roughly 1 hr & 30 min from the airport. Rental car or Taxi will be your best option.
From our past experiences in different countries it is best to have both. I would highly recommend going to the currency exchange before you get in Mexico and pulling out spending money in pesos. It is better to have the currency that the country you are in uses. If you plan to use your credit card, remember to let your bank know you will be using your card out of the country.