Welcome to the islands, and welcome to the forum
To catch some good fish I'd suggest you start off by learning out slowly by catching (and releasing) some smaller ones first. Personally I'd go for bottom fishing. Get acquinted with dangerous fish to protect yourself, especially skorfna which is somewhat common by the shore in the rocks (http://renotonna.yolasite.com/names-stu.php
As for equipment, start off by visiting a fishing shop (ask around there is one in rabat where there is arkadia if I remember correctly), get a small spinning reel (nothing fancy at first), a pole and fishing line to go with it (not wider than 0.30mm would do at first i guess), and then see if they stock ready made "pater noster" rigs. You will also need some lead weights and bait (from the fishing shop as well). The shop owner could also give you some basic tips and maybe point you to the right spot, but normally you can get something from everywhere.
For more advance techniques you can always continue to read this forum, and ask more questions as time goes by, but in the meantime, here is a very interesting read you might like. It has a wealth of information on local fishing and techniques, all of which comes from people who love sport fishing in Malta.
Click the first link that comes up.http://lmgtfy.com/?q=shore+fishing+in+malta#
some info i found for rigs used in malta from google:http://www.fishingmalta.com/sport-fishing/?fishing-info=rigs