First things first, are you aware that you only need the most minimal of spaces to make a complete bedroom? A 1x4 space is more than enough, with the first space being the door, the second being the bed, the third and fourth being a chest and cabinet (optional as im not sure these are working for non-nobles anyhow, but they will add value to each room and thus your fortress nonetheless). Your dwarf will have no qualms about climbing over/thru his furniture, and the door is nice so that you can lock him in if he gets pissy.
With this in mind, train your miners up to legendary by digging out all the necessary rooms for a proto-fort, preferably putting as much as you can in a soil layer(s), as they get the fastest mining xp digging in soil. I usually make a dormitory with 5 or so beds in the beginning, which is more than enough to hold your dwarves over in the meantime. In the future, you can remodel this room into a barracks for your military. Once they are legendary, carve out a massive pattern of 100+ 1x4 rooms down in a stone layer (layer 9 or below if you want to avoid woodcutting noise). At legendary skills, this will take your miners all of 5 to ten minutes real time to accomplish. Thats more than enough space for the first few waves of dwarves, and you can train your mason and carpenter up by spamming door and bed production to keep ahead of things.
When this floor gets near capacity, make a copy of it one floor down. Three such floors is nearly always more than enough to hold all the migrants you will ever see before a) your computer crashes or b) your fort meets its timely demise.
And once you have all those migrants? The worst thing is sorting them out, but definitely take the time to assign a committed workforce to different sectors. Get a military. Get some workshop dwarves and start up some industries. Train a medical staff. Get your farms and kitchens in order. Another pair of miners isnt a terrible idea, and you can always relegate the remaining hordes to menial hauling labors.