After the first exciting experiences you are finally set to get your first certifications !!! There are a few more steps to follow and you may soon become member of an ever-increasing international community of scuba divers.
Based on age and time available there are options in what you may decide to get while in Sardinia. In any case the progress is in steps and both ESA/CMAS and PADI both give you 2 options :

1) Certification to -12mt - recommended for the youngest and for limited time available - a course that takes 2 afternoons and 2 dives to include:
a manual/kit (paper and/or digital), simple and fun theory personalzed with the instructor 
Two dives in shallow waters to learn the necessary skills for safe diving
Two dives out at sea in close contact with an instructor
--- international certification to be able to dive anywhere down to -12mt together with a dive professional

2) Certification to -18mt. This course can be the continuation of 1) with another 2 or 3 days of extra training (in total 4 to 5 days to include first experiences) including :
a manual/kit (paper and/or digital), theory personalzed with the instructor and final exam
Five training sessions in shallow waters to learn the necessary skills for safe diving and autonomous diving (can be done in 2 days)
Four dives out at sea in close contact with an instructor (also possible in 2 days)
--- international certification to be able to dive anywhere down to -18mt indipendently

ESA training allows you to get at a small additional cost CMAS certification when required for institutional purposes (like public works, professional requirements, schools).