My advice to new players would be:
1) Everything you *want* to do when you first start playing is fairly irrelevant. Wells for drinking? Not necessary. Bedrooms for your dwarves? They don't really care. Beds? Furnture? Dining hall? None of it is important. You can make your dwarves sleep in rain, mud and snow...make them drink from the river even when it's running red with blood...no big deal. All that matters in the beginning is food. People will tell you that alcohol matters. It kind of does, but it's not as big a deal as people claim. No alcohol for your first year is fine. Again, all that really matters is food. Learn the interface, then learn how to make farms. Until you can do that, nothing else matters and your fortresses will be doomed to madness and death.
2) Do NOT try to make single dwarves that "do everything." Within a few hours of play you will have more dwarves than you can possibly use. Specialization is good.
3) You don't need two axes. Bring more food.
4) Don't get attached to individual dwarves, and don't get too hopeful about them becoming "Legendary." Dwarves will die in your game, fairly randomly, and very often there's absolutely nothing you can do about it. Plus, sometimes having Legendary craftsdwarves is more hassle than it's worth.
5) Don't get too attached to the idea of making an aesthetically perfect fortress. "Stuff" will get in the way and there's nothing you can do about it.
6) Many things that seem like they should be important...aren't. Or, are, but aren't important for your first few years of gameplay. For instance, when your first metalsmith shows up with a forge, completely ignore the forge and make him do something else. Forges, metalsmiths, jewelers, clothesmakers...lots of things: just don't bother until you know the game better. You can have a perfectly fun and long-lasting game with no industry other than: farm, kitchen, brewery, stonemason, carpenter, mechanic.
7) Hunters: nice idea, but they don't work very well. Don't bother.
Trade can sometimes be useful. But don't stress out over the "3-wide" road thing. It's just not that big of a deal.
9) Don't worry much about defense in your first few games. There's a lot of talk here in the forums about it because it's fun, but in all likelihood you'll have to spend years going out of your way LOOKING for battles before you have any, and when you do they'll probably be over before you can even find them on the map.
10) For your first few games...play on maps without elephants. "Elephant" is the dwarvish word for "Evil Tank."
11) Floodgates allow you to control irrigation for your farms. They are not neccesary, but they can be helpful, once you know how to use them. Save and backup your fortress before you experiment with them. If you don't get it right, your entire fortress will be permanently destroyed by a bug.
That list would have made my first five or six hours of gametime much less frustrating.