S-caliber, you have the right moniker. A lifetime is not enough to learn it all, so you have a lot to look forward to. As already mentioned, there are significant differences between Scuba spearfishing and freediving. There are huge differences in the habitat and reactions of individual species of fish. The broadest difference is between bottom fish and blue water, or "pelagic" fish. These live in their on worlds in their own time. The bottom fish are more likely to be at "home", under a rock or near a reef. The pelagic fish comes and goes. The bottom fish may be more wary as he likely sees divers, including spearfishermen, from time to time. With pelagics, you never know. Some, like certain jacks and cobia, are curious, or downright dumb. My favorite bottom fish are the tautog and sheepshead. My favorite reef fish is the mutton snapper. My favorite pelagic is the dorado (yum) , although the king mackeral and African pompano ain't too shabby either. The striped bass is in a class of its own.
The rubber band speargun is actually an offshoot of the archaic crossbow. Accuracy is not a process of sighting but more like the archer's "gap" shooting and it is a matter of practice. Try to learn with a particular type of gun. There are two types used by serious spearos, the rear grip arbalete type (arbalest=crossbow), and the mid grip "Addict" type. (The Addict gun looks somewhat like a bazooka). Both are rubber powered. There are many good guns around. JBL and AB Biller are popular. The JBL design is an aluminum gun although there is the recent mahogany 38. The Biller is available in a variety of fine woods. I suggest a metal gun for the bottom hunter and a wood gun for the freediver. If an Addict gun is desired I suggest the Riffe series, but bear in mind that this is really a freediver's gun and doesn't take well to bottom fishing.
Practice safe handling; don't bring a cocked gun on board. If you have a safety, use it. Remember, a spear is sharp even when the gun is not cocked. Mind the furniture, and the ceiling if it's a big one. Better, make a spear tip cover with a short length of latex tubing.