Antalya Airport is a modern, effective airport receiving a large percentage of charter tourists to Turkey.
It is the main airport for tourist destinations like Antalya (20min west), Kemer (1hour10min southwest), Side (1h15min east) and Alanya (2h30min east). Also Kaş (3h30min southwest) and Kalkan (4h southwest) can use Antalya, but for these Dalaman is perhaps a better option.
There are several companies offering car rentals from Dalaman, either organized at the spot or beforehand. As to what gives you the best price, there is no absolute. Out of high season, arriving in the middle of the day, you have a good chance at getting a nice discount. Several local companies offer pre-booking of car, in most cases this is both safe and easy, but on one occasion I experienced that the booked car was not there.
Should you need accommodation before or after a flight, there are a large selection of hotels in Antalya proper, as well as in Lara, the tourist town right south of the airport.
The airport has several tax free shops, alcohol, perfume and tobacco is reasonably priced. Others shops specialize in selling exactly what you just saw in the tourist bazaars but at inflated prices. Note that when you pay with credit card, the indicated prices in Euro are paid in Turkish lira, and at a slightly unfavourable exchange rate.
The nearest international airport west is at Dalaman.

Visit the website for Antalya Airport.