Here are a few basics about some of the more popular smoke woods. But, you may be better starting a new thread -- it's a big topic and should receive a lot of input and attention.
The wood menu in this post represents of the woods you're most likely to find. But there are others -- and my discussion is by no means complete or inclusive. When you have questions about any other, you can look it up online. There are a number of tables posted -- and most of them agree as to the major points. Kind of amazing, really.
You'll find a lot of great information here, BBQ FAQ Forward
. The FAQ is a wonderful source with a single caveat. It's dated -- especially as to equipment, but methods too. Time marches on and techniques advance.
Another good sources is, The Virtual Weber Bullet - For the Weber Smokey Mountain Cooker smoker enthusiast
. Although it's dedicated to the Weber Smokey Mountain (WSM), there's a lot of good information. Bear in mind, the technique and information guides on the site are good, but not gospel.
The most popular strong woods are hickory, mesquite and red and white oak. Like many smokewoods, all three have regional associations: Hickory with the south; Mesquite with the southwest; red oak (and live oak!) with California, and white oak with parts of the midwest.
A few woods are too strong to control easily, and should be avoided until you have a very good idea of what you're doing. Walnut, for instance.
Some popular medium woods include alder, apple, cherry, citrus, grape cuttings, maple, peach, pear and pecan. Almost any fruitwood fits into this category. Some have strong regional associations, others are liked everywhere.
Sometimes Americans (and Canadians, too) get the idea that cooking with smoke was invented in this hemisphere. Not so. You can figure out which woods were and are popular in which countries, by their regional associations. Oak and cherry are bothy very popular throughout northern Europe.
I'm not going to bother listing very mild woods -- for one thing, you can get better flavor with a strong, mesquite charcoal; for another, if you're using charcoal for heat and wood for flavor (which is how the most popular smokers work), the charcoal will overwhelm the wood.
You'd already figured out that each wood has its own character, and some work better with some foods, or you wouldn't have asked. Yes. But... (I hate that "but" as much as "it depends.") It depends. (Dammit!) Among the various factors to consider is what type of cooker you're using, what kind of fuel it burns to make heat, and how well it and you can manage the fire. Without knowing those things, it's hard to make spot on recommendations. Also, a lot of differences assume bigger proportions reading about them, then they do in properly cooked food and can be "distinctions without a difference," as the saying goes. Take it all with a grain of salt, and preferably a dry martini.
Getting to brisket (at last) specifically... Beef likes strong smoke. Since southern barbecue is traditionally pork, you can infer that hickory is not a "traditional" wood for brisket. If you do, you're right. That doesn't mean it doesn't work though. But it's not among my first choices.
Barbecued brisket, as we know it, started pretty much a Texas phenomenon. Mesquite was and is the choice in Texas 'Q. Beef in general and mesquite in particular tolerate strong smoke. Mesquite is a strong wood, so there you go. More generally, mesquite can be used to smoke any food. You do have to moderate it somewhat, by limiting the amount of time you burn smokewood, and/or by mixing it with a milder wood. When it comes to brisket, mesquite should always be among your first choices.
I'm from California, have spent a great deal of time, and sucked up a lot of calories in the central coastal valley area where "Santa Maria Barbecue" was born. Actually it should be called California coastal valleys barbecue, but don't get me started. Anyway, we like oak. We especially like red oak and live oak. But for most people, when it comes to cooking in a regular "smoker," white oak is close enough. Oak smoke has a rounder, smoother characeter than the sharper mesquite. It's not quite as strong, and is the best all 'rounder. Great for brisket.
Cherry is a good choice, but a skosh mild for beef. Mixed with oak or mesquite -- wonderful.
Maple and maple/pecan are my first choices for lots of things. For beef though, I like to mix maple with any of the big three (hickory, mesquite, oak). And yes, even hickory/maple is a great combination for brisket.
Hope this helps,