I always bring one miner. I always regret it and wish I'd brought two, but I don't really have the dwarves to spare. Sometimes for dangerous embarks I double up spare miner/hammerdwarf, but that is a bad idea(picks).
The essentials are usually 1 miner, 1 appraiser/diagnostician/carpenter/mechanic, 1 craftsdwarf(usually bonecarving mostly, but he gets all crafts turned on for the first year or so), one general farmer with everything under farming, and one specialist that does planting and maybe brewing and nothing else. That makes five, and having a mason/bowyer/woodcutter is nice. Also having someone with one rank in ambusher, just so they can murder the wildlife.(also sometimes you get a crossbow and some bolts that are metal, which you can melt down and replace with wooden ones if you're quick) If there are surface metals I'll make a weapon/armorsmith sometimes.
I specialize a lot for the embark I'm going to, though. If there's even a trace of a haunted biome(which there should be, because they're really handy/FUN) one guy is getting a silver warhammer, a copper hat, and discipline points. (Also the butchery/tanning/furnace operation/pump operation labors, because those train spatial reasoning and strength). I always forget to make spare pants/shoes/shirt before turning on replace instead of over, so he's always unhappy because he's naked OR he's not wearing his hat.
I always forget to bring a quiver and crossbow, or I can't afford it. Drop a little dough on turkeys though, those are a great investment. They cost one point more than the leather they really represent, but you get fat and meat and bones and a neat little trinket to sell off packaged with the leather. Cats are great, even if you only bring one. The vermin remains are annoying, but the vermin themselves are worse. Dogs are excellent anti-thief protection. Chain one outside your door!
I've tried doing minmax embarks where you bring like five bits of gabbro, some ore, and some lignite and forge your picks and axes, but I nearly always screw it up somehow. I end up with like 30 lignite but no coke to kickstart the process, and no axe to cut down trees, and I haven't brought wood. (in retrospect should have busted up the wagon for logs, made a training axe. Poop.)