My advice, with pictures:
1. Use Dwarf Therapist. Unless you're masochistic, it's the only way to properly manage your dwarves and the flood of migrants. What I do is when a new wave of migrants come in, I pause the game and examine them in Dwarf Therapist.
First thing I do is pick out those who are
very good at something. I usually disable hauling and other manual labor for them so they can focus on their specialties and not get killed by randomly going out in seiges to retrieve tattered socks. These are the elites and will become legendary someday. They help the fortress by churning out high quality items for trade and to keep my other dwarves happy.
Next I pick out the dwarves I need from those showing an inclination for it. For example, I need two more miners, so I pick two dwarves with the highest skill points in it from the group. I also examine them for military suitability. Those with martial skills (or at least are strong or agile) get assigned to my squads, replacing earlier additions who aren't as skilled if necessary. Don't worry if none fit the criteria yet, pick one at random, you can replace them later on when the next migrant wave comes.
The rest of the group I set to hauling/cleaning/tending animals/harvesting only. I disable all their other jobs if they aren't good enough so they won't waste materials on their low quality stuff.
2. I divide my fortresses into several parts. Each with elements that work better close together.
First is the entrance, which includes the trade depot, barracks, hospitals, cages (for animals and captured enemies alike), and stockpiles of items I intend to trade away. It includes the most important part of the fortress - the gate. It must be well fortified. Wide enough that it can allow trade caravan wagons to enter but also it must be easy to seal everything at a moment's notice. I usually do this using a zigzagging 3x3 road interspersed with stretches of traps and a series of drawbridges. A variant of the "airlock" design.
Second are the living areas, which include multiple levels of bedrooms (they take a lot of space). Above them are the kitchens (including fisheries and butcher's workshops) and food storage areas (along with poultry and nests for quick harvesting, and pens for non-grazing food animals like pigs), and the dining halls. This is the heart of my fortress, with everything else radiating from it.
Third are the noble quarters (usually on the highest levels of my fortresses), with the throne rooms, recreational areas (sculpture gardens, etc), and wells.
Fourth are the workshop areas. Usually I place these a few z levels below the living areas. These are square rooms with different workshops in the middle and immediately behind them the stockpiles for raw materials. I may also dig up multiple layers of additional stockpiles below them.
Fifth are the farming areas. These are usually aboveground or close to the surface. This has pastures, fields, seed stockpiles, and when my fort is old enough, mushroom fields where I let them grow out to provide me with lumber. I may also divert a water source here, build a well and a fishing area.
Lastly are the catacombs. I usually place them in a single level, somewhere below or away from everything.
This is all just a guide for me though. I may vary the designs when needed to suit terrain or aesthetics. Because at the end of the day, the only thing that matters is the gate. How you design the rest of your fort is up to you really. In my fortresses for example, every dwarf gets his own room (a 2x3) with his own cabinet, bed, door, and chest as it keeps them happiest. But other players use communal dormitories which is cheaper and keep them happy by other means.
Note that I don't build them all at once. I build the basic ones first but leave enough space to add the rest of the elements of each fortress "subdivision" as I need them.
3. Treat wardogs as disposable early warning signals. Same with cats. The only people I have wardogs assigned to are those which have to go out at times (e.g. woodcutters, beekeepers) to keep them a bit safer. They breed too quickly to mourn their passing much, so don't. Extra animals you butcher. But keep a breeding pair or two always. Both turkeys and dogs don't need to graze, so pasture them in separate areas anywhere you like (preferably out of the way of heavy traffic to avoid people adopting them). And regularly cull the group for meat. I also separate female poultry and give them individual nests for eggs.
4. Once you have a fairly stable bustling fortress, start building, improving, beautifying, and experimenting. Explore caverns, branch out on a new industry (try giant cave spider silk farming for example), build better quarters, pave roads, tame and breed exotic cave animals for war or food, device nefarious new traps to kill invaders, build a tower made entirely out of gold, etc.