On the first day it's too late to go on a tour but you can easily see the area on your own. You can take a local bus to Zelve open air museum (one of the best sights!), then walk back to Pashabag, and Cavusin and in the afternoon go to Göreme open air museum. The next day you can take the Green Tour to Ihlara vallley, Derinkuyu underground city and Selime monastery. I recommend New Göreme Tour, I have been on very nice tours with them.
You should definitely book a shuttle in advance from Nevsehir airport to Göreme, it will take you directly to your hotel. At the airport you can either take a taxi (very expensive) or a shuttle to Nevsehir bus station, but in order to get to Göreme, you have to get from bus station to the centre, where Göreme buses depart. Ask your hotel to book a shuttle for you or contact the shuttle company, Cappadocia Express.