What is the best way to travel from Barcelona to Girona? And, do you have rental car recommendations in Girona?
There's excellent train service. You can choose from an express train (usually costlier) or a slower train (less expensive). Fares on express trains vary wildly by departure date/time and how far in advance the purchase is made; you can often save a lot of money by buying those tickets early, but observe the refund/change policy. Check schedules at https://www.renfe.com/es/en; remember, the express-train fares may be different tomorrow. The fast trains take about 40 minutes; the slow trains, between 70 minutes and 2 hours.
I have never rented a car in Europe, so I have no personal experience to offer on that topic. However, many posters have used one of the rental-car consolidators (AutoEurope, Gemut or Kemwel) and been happy with the service and the price.
If you drive, Tossa de Mar is a worthwhile short detour.