1. As others have said, local dive shops are probably the top of the list. If you're in school (college), there might also be a diving program there as well. As far as agencies go, my wife and I were certified through PADI (there, I've said it).
While others aren't exactly enamored with their program, I think that the responsibility for becoming a good, safe diver relies more on the diver than anything else. There was another couple in our class who I would not feel comfortable buddying up with. Did they pass? Yes. I feel that PADI provided (through videos, books, classroom and in-water training) us with a good start, and presented sufficient information for us to be safe divers - when diving within our training limitations. I think that the people who get into trouble are the ones (like that couple in our class) who see the certification courses as a hurdle they have to get through to be able to go on their dive vacation, as opposed to opportunities to learn. While some of the skills may seem odd and unnecessary (replacing your weight belt while underwater was top on my list), the knowledge that you have done it and the confidence that it gives you are what's important. If you have any problems with skills, be sure to go over them with your instructor until you have them down pat.
2. As far as questions go, ask about anything you can think of. Quite a few times, our queries were momentarily greeted with that "Who doesn't know that?" look, but both the LDS employees and instructor were happy to explain anything and everything. Quite frankly, I would at least ask some questions of the dive shop and instructor, if possible (we didn't meet our instructor until we showed up for class, however). Like anything else, you can get a feel for the type of people they are, and whether or not you feel comfortable with them. If they seem annoyed at your "beginner" questions, or just seem to be pressuring you to sign up for the class or buy stuff, then you might want to look elsewhere.
I think it's important to develop a good raport with your LDS. The idea is that you spend the bulk of your equipment and training dollars with them, and they in turn are there to answer questions, give you "loyal customer" discounts, and handle any equipment problems you run into. Find someplace you're comfortable with, that seems to have experienced divers as employees (as opposed to travel agents), and that has a relatively good selection of equipment.
3. Well, if you have to ask.....
I don't have all the figures in front of me, but our "startup costs" were a bit substantial. Of course, all the equipment we ended up liking ended up being the expensive stuff, and we needed to get a prescription lens mask for my wife. But hey, your life may depend on it, and if you take care of it, you'll only have to buy it once, right? Just be sure you don't try to cut corners and buy a cheapie mask/snorkel/fin kit from Wal-Mart or a regular sporting-goods store. These are *not* the same thing as the expensive stuff at the dive shop. Take a look at each, and you'll see what I mean. Assuming you go to a reputable LDS, all the equipment they sell should be of decent quality.
4. As far as dive equipment, we were encouraged to get masks, snorkels and fins. For the classroom, we got the basic open-water book from PADI (if you go PADI, I'd recommend the book over the CD-ROM version), and borrowed the video.
5. Not really. Be sure to study the classroom material before class - it's really not all that difficult, and it gives you a chance to ask questions during the class as opposed to trying to learn it "on the fly." Oh, depending on your level of fitness and swimming ability, you might want to get in some pool time swimming laps before the pool sessions. I hadn't even been in a pool for about seven years. Swimming was a lot more exerting than I remember! The swimming requirements (for PADI, at least) are pretty trivial, but it was still nice to get used to the water once again.
If you're not 100% sure that you want to get into diving, one thing you might check on at the LDS is whether they have a "Discover Scuba" class. Our LDS does this for free (which is a nice bonus!) I'm not sure what all it entails - I think some classroom learning followed by time in the pool with scuba equipment. This will give you a small intro. to what diving is all about and will let you see if it's something you want to pursue. They supply all the equipment (including mask, snorkel, and fins), so if there isn't a charge for the class, you're not out anything if for whatever reason you don't like it. The Discover students were in the pool when we were there trying out some new equipment, and seemed to be having a good time - they just have you swim around - no skills tests or anything. Just fun.
As others have mentioned, have fun! There will probably be a skill or two that will give you trouble at first - seems everyone runs into a problem or two. Just stick with it, and you'll be fine - the rewards of diving are worth it!
