Two miners is usually enough for most fortresses. Depending on how much mining you do, you can get more miners whenever you feel like it.
As for your mining; some maps can be thousands of levels deep. Just keep digging and you're bound to hit some metal.
Thousands??? I've never seen much more than a hundred. I suppose one could use advanced worldgen params to get more, but I have never heard of an unmodded world thousands of levels deep.
Since it's mid-autumn, you should have the first dwarven caravan in a week or two, so you can buy one from them quicker than you can find ore, mine it, smelt it, run out of charcoal while smelting, cut more trees, make more charcoal, and forge the pick.
But you'll still want to get that metal industry going before long to make armor for your troops. So doing some exploratory mining is still a good idea. First off, make a few rock hatch covers. Then send a stairway down as deep as you can. You can designate a stairway quickly by doing 'd' 'i', then put your mouse pointer at the place you want the stairs and press and hold the left button down. While holding the mouse button, press and hold '>'. As you move downward through the levels, the up/down stairs will get designated for each one. You can go ahead and designate until it won't go any deeper, but I usually just go down 50 or so levels because I usually hit a cavern before then and I don't like having to go back and undesignate dozens of levels to clean up. Then let a miner start digging until you hit a cavern. When you do, assuming you hit the top of a cavern. dig a tile sideways and build a floor hatch on the bottom of the stairs to seal it up. Once the hatch gets built, select it with 'q' and then hit 'l' to lock it. Now fliers can't come up from the cavern. If you happen to hit a cavern by grazing the side, you'll want to build walls to seal the stairway from the cavern. If you hit a cavern and can't continue straight down, just dig to the side until you can go down again. Eventually you'll hit semi-molten rock (SMR) or the magma sea. If you hit the magma sea, put another hatch cover in place for now to keep magma critters out.
At some point along this stairway you will very probably hit some sort of metal ore. If you hit caverns, you'll probably see ore veins in the cavern walls that will give you a good idea where to look. Digging down 100 levels doesn't take much longer than digging out a 10x10 room in rock. But it will give you a good view of what layers you have, and probably find some ore.
I usually start with 2 miners, and eventually add a couple more over time. If a migrant shows up with decent mining skill I'll definitely use him. Otherwise when I decide I need another I'll pick someone with no useful skills and give him the job. Then I turn off mining for my skilled miners and designate a large room in a soil layer to let the newbie get some experience. It sucks when you spot a nice gem and designate it for digging, and your rookie runs over and ends up botching the job and not leaving a gem behind because his skill is too low. So always find someplace to train them up where you don't care about getting stones/ore/gems from the digging. Soil is good because it goes quickly.