Well, I've done this a few times and loved it, so I'll take a stab here. I'm not a pro by any means, though, so you're just getting my observations.
First, there's a lot of range. I gather you're fishing in the Gulf of Mexico, which is where I've done most of my deep sea fishing. You can go on a big charter boat with 50 other people, or you can be a private boat owner with a motorboat and a Saturday off. You can target the big game fish, which seems to mean trolling, and therefore not much chance of catching anything else. Or you can park in a good spot and fish for something to eat. I prefer the second option -- you've got a much better shot of catching something, and still a pretty good chance of catching something fun. The times I've gone have been on a medium sized motor boat (comfortable for four to six people), but with two heavy duty engines (the best fishing is often a pretty good ways from shore).
As to gear, you'll mostly want heavy rods, although it can be pretty exciting to catch a big fish on small gear. Since it's deep sea, you'll need reels that will hold a good bit of line, preferably of a heavy test weight. For best results, you'll mostly be using cut bait.
As to the fish, if you're fishing in the Gulf, you're in luck -- there's all kinds of great stuff out there. The best eating fish mostly hang out near the bottom, and like structure -- an old wreck, or a reef, or some such. There's a number of artificial reefs in the gulf, sunk to attrack these fish. This is where you'll likely pick up red snapper (and a few other varieties of snapper), grouper, or trigger fish. Those are all terrific eating, though the trigger fish is a very delicate meat (ironic for a member of the piranha family). Fishing closer to the surface, you've got a shot at things like king mackeral (I don't care for that one -- very red, oily meat), which can get pretty big and give a good fight. Last time I was pulling in one of those, we had barracuda hanging out near our boat that tried to attack my king mack on the way in. We ended up catching one or two of the barracuda too. I wish we'd kept them to eat -- slight risk of poison from their meat (one of their preyfish eats a poisonous shellfish), but it's supposed to be a really good meat, and the poison isn't all that dangerous. One of the best fish out there is mahi-mahi, also known as dolphin (to be distinguished from what most people call dolphin, which are actually porpoise). As small fish, those school and like to hang out underneath surface clutter (like driftwood). Since the keeper size on these isn't really that big, you can get them at that size easiest, probably. As they get bigger, they separate from each other and become more free-ranging. They're beautiful fish, can swim somewhere in the vicinity of 50 knots, and are terrific eating.
There's other fish out there; I can't even remember all the ones we've caught or seen. The season in which you fish will determine what you're after and what you can keep. You'll probably see bottlenose dolphin all too often, and after you get over thinking they're so cute, wish you could get rid of them -- they eat the same fish you're fishing for, so you have a terrible time getting anything into the boat when they're around.
As to the shark, we never targeted them specifically (though I've always wanted to catch one). Generally speaking, they're not the best eating in the gulf, and some are downright terrible. They're a fun gamefish, I guess, but no better than tarpon, say. Possibly the most common out in the Gulf is the hammerhead, which looks horrific, but isn't terribly dangerous, as sharks go -- you're safer around that than you are around those barracuda. Often you end up with a shark by catching something else like a snapper, and then having the shark grab that as it goes by. The charter captain we use talks about a group that pulled up something like a 500 pound shark that way. Of course, that's way too large to get into the boat; you just have to cut your line.
Hope some of this helps.
