Not a silly question! I had the same questions, and I took a lot of time (and fun) to do the research. Again, I’m new to it, but I think my research seemed solid and brought me to some valuable conclusions. There is no doubt that someone will jump on me if I stray too far, so here’s what I found….
You will probably buy your regulator and vest for two reasons, comfort and reliability. You will be surprised and delighted when you compare a poor to average regulator or vest with a really nice one. The ease of breathing is the primary benefit for your regulator, usually due to the construction if not the fine-tuning adjustments. Better vests have multiple dump points, as well as other goodies.
The regulator usually (if not always) comes with the “first stage.” This is the part that connects to the tank. Depending on the cost and quality of the regulator, the first stages will also have their differences and benefits as well (e.g., the number of ports for future hose attachments). Now that you have your primary air source (regulator), you still need to have an alternate air source. These come in two forms, the octopus or “octo”, which is an additional hose coming off of the first stage, usually yellow (for easy identification) it usually fits under your right arm, and the integrated alternate air source, which has a mouthpiece in your short BCD inflator hose on your vest. (There are four pages on which is better on a fairly new thread). Here's the point. If you go with the octo, you buy a regulator, and octo, and a pressure gauge/computer. (You will need to buy them all at one time, really. I don't think that you can rent "just a pressure gauge.") You can mount this hose package on any rented tank and vest and rock on, being free to buy your vest later (or visa-versa). But if you want the integrated alternate air source, you kinda need to buy them both at the same time, because the vest's inflator hose is your alternate mouthpiece. It would be awkward to buy a regulator, pressure gauge and no octo…..until you have a vest that has an integrated secondary source? That hose combo is awkward if not impossible to functionally use when you are renting a plain vest. Or, let’s say that you buy a vest with an integrated secondary air source. You’ll have to rent hoses that support that set up. If you go with an octo, you have flexibility to purchase slowly. If you go with the integrated alternate, it may be easier to buy the hoses and the vest at the same time.
Vests. There seems to be two primary styles of vests, full jacket, and back inflation. These refer to the air bladders inside. The vest style surrounds you more with air. It is usually easier (so I’ve heard) for many nubies because it is easier to control buoyancy both under the water as well as when you are on the surface. It is generally easier to stay upright. The back inflation is a very popular vest with many divers because you can plane easier and it is less cumbersome. Many schools teach primary classes with back inflation vests. The thing to realize is that air goes up. So if you have a head down or sideways attitude, you will need to maneuver yourself to get the air where it needs to be in order to vent it. Again, this is not a problem if you are talented, experienced, lucky, or have a great instructor. It may not be a problem at all. The point is, know the advantages and disadvantages of each, depending on your comfort level in the water as well as the kind of diving you eventually want to do.
But most important of all…make sure your LDS (Local Dive Store) asks what kind of diving you are going to do!!! Hiking in the desert uses very different gear than hiking in the mountains! Diving cold water is very different than diving warm water! A kick-butt warm water reg may freeze up in cold water! Make sure that all of your hoses compliment each other in function (not just in color, for heaven’s sake). Whether you're buying SCUBA equipment, stereo equipment, or investments, if your sales person is not asking you questions about what you want to accomplish, RUN! [sales person in a stupid voice,] "Well, we have this package over here..." AHHH!!!! BS!! BS!!! It may be great, but know why it's great for you!
Last piece of advice. Be careful about buying complex equipment on line!! MANY MANUFACTURERS WARRENTIES ARE NOT VALID UNLESS PURCHASED THROUGH AN AUTHORIZED DEALER. Many items are not to specs when shipped from the factory! Most dive stores will cut you a deal if you buy regs and a vest that are within $100-200 of what you would spend online, and the support is invaluable!!
Have fun researching! Read. Read a lot! Go to different stores and ask the same questions. Then start to build your questions on the past answers.