Having played since 2D, I've fallen into a typical pattern for my forts which I only rarely deviate from. so there's not much planning, though I am pretty specific about embark locations. I usually re-roll worlds until I find that perfect spot, with both magma and running water. Other stuff is a bonus but it MUST have water and surface magma.
After that it's easy since I just use the setup I've used for a decade now:
a) dig into hillside, or straight down if no convenient hillsides are around. First a 5x5 room for the trade depot (with a 3 wide entrance), a narrow winding hall to a small barracks. Early, this barracks is the communal dorm; later it becomes a training and sleeping room for the militia.
b) A downwards staircase off from the entrance lobby, which branches into a x2 or x3 wide hall heading either east-west or north-south. On either side is four shift-diagonal'd storage rooms; these are always Wood, Furniture, Finished Goods and a general stock for everything but food. (I also always chop off a 3x3 area of the Finished Goods and replace it with a 2nd one, this one only accepts stone goods while the other forbids it-- this means I can crank out stone crafts and pick them out easily for the depot).
c) At either end of the hall, staircases down. These, and the main hall, continue downwards until I hit stone.
d) On the next level, 4 more 11x11 (or is it 9x9 for shift-diagonal? Can't recall) storage. Two food, one refuse, one becomes a farm.
e) Next level, 4 more 11x11 squares, only I chop them into 5x5 chambers by removing the mining designations through the middles. These become workshops, all are set to be as close as possible to the appropriate storage. Since not all workshops will fit in 16 chambers, the next few levels are reserved for more as they are needed, but only the hallway is mined.
f) 4 or 5 levels down (or when I find a nice vein of ore), the two up-down staircases become one down staircase in the middle of the hall. This level becomes the social district - a large (at least 11x11) dining hall, small prison, hospital, graveyard. Also, down a long, trapped corridor are the treasure chambers; one room with a barrel-less stockpile that only accepts artifact-quality items, another only accepts coins. Looks fancy when they're all arranged on the floor!
g) Down a few more levels, government rooms. Expedition leader's chambers, throne room, noble quarters; typically these are lavish and branching, and always at least 4x4.
h) Down a few more levels (typically, just before the caverns), the apartment complex. In earlier days I would make large, 3x3 rooms for every dwarf, but lately I just make big, elaborate dorms and put 4-12 dwarves in each one. They still seem pretty happy.
I only rarely ever use traps, bridges, moats, or walls for the front door, instead relying entirely on militia and crossbows -- since I let the elite masters do all the work it leaves me with an enormous pile of unemployed. If there's a tantrum spiral I let it work itself out, and the survivors carry on and rebuild. It's actually very rare for the entire fort to be lost.