Well, it depends on how much you want to get into it. I would definately buy my own mask, fins and snorkel. However, if you go on dive trips you can rent all of the equipment. However, I bought mask, fins, snorkel, regulators (mouth pieces for the air), BC (bouyancy compensator), computer(which has your gauges on it), wet suit and/or skins, gloves, light (for night dives). I think that is about all of the important equipment that I bought. I did not buy the tanks and weights, seeing that when you travel to go diving it is just too heavy to carry and you can rent this cheap enough.
I hope you are planning on taking lessons and getting certified, which you have to be in order to rent equipment.
Diving is a great sport, hope you enjoy it.