In my opinion a handspear is fine to start with, the thing that you should make sure you dont miss in your starting kit would be to have a float line and float with dive flag to make boats aware of your presence for safety reasons, im fairly new to diving up this way (port phillip bay) but i have seen both jetski's and boats come fairly close to me at speed when im in the water. other than that there are the usual items; a wetsuit (prefferably), Fins, mask,, snorkel, wieghtbelt (with the right amount of wieght), Knife (for ikiing fish and for safety too). There might be some stuff i have missed and sorry if i have, im sure some other people will have more to add
Also do a search on the forum as im sure there would be more posts asking the same sort of thing. Hope this helps