First, thanks to Shozab Hasan and user359650 for these tests. I was wondering which choice was the best and now i know:
To encode a simple array, JSON which is OK with both PHP AND javascript, maybe other languages.
To encode a PHP object, serialize is a better choice because of specificity of PHP Objects only instanciable with PHP.
To store datas, either store encoded datas in a file or use MySQL with standard format. It would be much easier to get your datas back. MySQL has great functions to get datas the way you'd like to get them without PHP treatment.
I've never made any test but i think that file storage is the best way to store your datas if system file sorting is enough to get back your files in alphabetical/numeral order.
MySQL is to greedy for this kind of treatment and uses file system too...