The easiest airport is Alicante and can be reached by most regional airports, the main airlines that fly here are Ryanair, Easy Jet and Jet2.com.
You can also fly to Murcia and Valencia although you will need to hire a car from these airports as they are both over a 2 hour drive.
There are plenty of hire car companies too with the most popular being Gold Rentals and Record these can be both found inside the airport or on the internet.
If you are not hiring a car there are other ways to get to each resort, the cheapest being the Alsa Bus which you can find by clicking this link: http://www.alsa.es/en/ however depending on your flight arrival the last bus is usually about 7pm, if this is the case there is also BeniConnect which can be found on this link: http://www.beniconnect.com this is a good reliable company that charge approx. 38 Euros return to each resort with certain drop off points in each area and they also cater for late arrivals, you can also book private hire with this company and all the prices are on their website. The journey takes approximately 2 hours 15 mins.
If you are travelling by car here are the directions from the airport to Calpe: http://www.spainairportcarhire.com/driving-directions/alicante/driving-from-alicante-airport-to-calpe.php#directions