Our personal preference is a self catering apartment as you can feel 'over blown' with food in hotels and AI - I don't think you would eat that much food at home! It is lovely to be able to make yourself a cup of tea just when you feel like it and a homemade sandwich or good old beans on toast can be very welcoming!!! Also, there are so many good cheap bars and places to eat you will make a lot of new friends whiling the time away with a coffee and brandy and many of the bars have english daily papers to read. At the end of the day, it's your preference but whatever, I'm sure you'll enjoy it.
NB Generally, if you book an apartment through a tour operator, they generally charge based on 4 sharing . Better to book independently. Gestaltur is a reliable Benidorm agency but a quick search engine "self catering accommodation in Benidorm" will bring up loads of possibilities. Good hunting!

Also try http://www.beninter.com
They have some great apartments to rent.