I never had such a big problem with immigrants unless I'm unlucky enough to have them arrive during some other disaster. All you have to do is mark about a hundred rooms for digging out near the beginning of the game, set dwarfs on repeat-building beds and doors forever, and constantly expand your farm.
Remember when setting up your farm at the end of each winter that it is extremely easy to dig out a little more and make your muddy area bigger, but extremely hard to enlarge it during the rest of the year. Make it as big as you can possibly imagine yourself needing, then double that size, and increase it by a sizable amount over that every year. If, at any time, you notice that your entire field is getting planted, double it in size the next winter. Set your farming dwarves to do nothing but farming during any season but winter; if they're ever idle, you need a larger farm. If they're never idle, you need more farmers. Assign a fixed percentage of new dwarves who arrive to farming, and never, ever, allow a new wave of immigrants to enter without setting at least this percentage of them to full-time farmers. And so on. You can never, ever have enough food. If you are doing it right, you will need at least one dwarf and a workshop devoted entirely to spitting out barrels to support this; your food supplies should be going up madly during any season but the winter, and should be increasing overall year-to-year almost as fast.
You will probably want to give your farmers other tasks during the winter, of course, but don't forget to switch them back later.
Oh, and one other thing. Your dining room. It's actually one of the easiest places to screw up, which is a shame because it's actually very easy to handle. Just make it large. Bigness will increase its value and let you add more table-and-chair pairs (only one chair to a table!) You should detail it eventually, too. Dwarves visit the dining room regularly, so a little bit invested there can buy you a lot more goodwill than effort wasted somewhere else.
Wells are one other place that tend to get overwhelmed. As your fortress gets larger, you'll need wells everywhere... don't forget to put traps around all of them to catch anything that crawls out.