I'm not exactly new to the game, but I'm still absolutely terrible at it and I've gone through about over half a dozen forts all ending in the same boring un-fun way:
Start Game
Set up farming
Set up craft stations
Set up bed rooms
20 Immigrants arrive, all of useless professions
Attempt to up more bed rooms
While others have noted that you don't *need* bedrooms at the early stages of a fort, let's look at what you might do. You've just gotten 20 more dwarves, and based on your previous experience you'll get more dwarves again in several months. So, let's assign some relevant jobs to the newcomers; just off of the top of my head, how about (and all of these are in addition to whatever your original 7 were doing already):
2 miners
7 haulers: 2 general-purpose (all hauling enabled), 2 specifically stone, 2 specifically wood, 1 specifically item
1 "door-maker" (either mason or carpenter depending on what you want to make them from)
1 "furniture-maker" (tables, chairs, misc; either mason or carpenter depending on what you want to make them from)
1 "bed-maker" (carpenter)
2 wood-cutters
1 weaponsmith, if you don't already have one (to make some spare picks and axes)
1 backup brewer (with their own workshop for redundancy)
1 backup cook (with their own workshop for redundancy)
1 backup farmer (with a second small farm for redundancy)
That takes up 18 of your new dwarves, and should be pretty close to what you need to dramatically build out your living quarters (barracks, bedrooms, dining rooms, etc.) in *far* less time than it takes for another set to show up. Dwarves are the engines of your fortress; to put it in Civilization / Master of Magic terms, they *are* the "hammers" or "shields" that you use to make things. If you're short on raw materials, assign another miner or so for exploration, and/or some dwarves to smelting and other back-end tasks; if you're in a hostile environment, start training some as early military, or set up a workshop flow for traps; and so on.
Again, this is not a prescription; you've been given a huge boost in productivity, use it to be productive. DF is intended to be a "learn by failing" game, to some degree; like classic Roguelikes. In Angband, if you find your high-score list starting to be dominated by deaths to poison, learn to not go below 2000' without a source of Resist Poison. In DF, if you find you keep getting large migrant waves, use the first one to build out your residential and service infrastructure.
Changing the pop-cap numbers may be useful as training wheels, or to force smaller games due to preferences or hardware limitations. If you don't want even a mayor at first, set (for instance) soft at 35 and hard at 45 until you feel you've got things initially organized, then perhaps take it up to around soft 65, hard 75 and stabilize things there until you're ready for more complex interactions. There's no reason not to adjust the pop cap during a fort's lifetime to match your intentions, inclinations, resources, and/or ability at that particular point.