On driving: Selcuk to Cappadocia is a long, long, long drive via the coast. Well worth doing--for the record, we've done exactly that drive--but over quite a few days. You would be best off renting a car in Izmir. The critical question is what the drop-off fee would be for leaving the car someplace other than where you picked it up. Most international companies charge a hefty fee to do this. A travel agent based in Izmir could steer you to a Turkish car hire place with offices in Cappadocia as well. When we did this route, we got a quote with no drop charge at all.
Renting a car in Fethiye and going to Ankara gives the maximum degree of flexibility along the coast and lets you see places that would not be worth going to if you had to go by bus or dolmus. For example, Patara is a gorgeous golden sand beach, a rarity on the Mediterranean coast. But going there by public transit is awkward because you have to fit your visit to the timing of the busses or dolmuses. By car, you arrive when you want and leave when you want. Likewise, Myra has impressive cliffside Lycian tombs. But by dolmus from Antalya, it's a long-winded hassle to get there. By car, it's a snap.
Also, as you are traveling along the coastal road, there are drop-dead gorgeous views where you can stop and admire (and take photos) from pullouts if you are in a car--in a bus, you grab your camera only to miss as the bus goes by.
I'd highly recommend a car for the coastal route, again watching out for drop charges in any quote you get.