A single Copper Pick, or one Iron Anvil and one Copper Nugget to show off, plus whatever you find uninteresting to make yourself.
On tame embarks you don't even need that, as the wagon comes with 3 wood (for a training axe and infinity wood), plentiful bone bolts, meatstuff for food to trade, tallow for soap, 2 leather for quivers, and some hair for thread at the hospital. Once you kill a few things with all your new wooden crossbows and bone bolts (for more leather quivers), you'll be busy enough without all that digging nonsense.
Should you have the Anvil, max Animal Training, and max Mechanics can earn some early pets, or the Hunting/Archer stuff to speed that hunting along if stuck up top, or at least max Architecture for making a nice trade depot and someone as a good trader so you're rich in the first year rather than the second or third. A good Herbalist brings in time-saving stacks of food, as a Fisher does with Fish, and a good Cook makes you the richer with all of them. If you want your early beds and tables to be nice ones, a Carpenter and Mason will do that.
Immigrants cover everything else, and dabblers train up soon enough where they don't. With the slightly challenging embarks where it rains blistering and vomitous contagion on the walking dead over a salty aquifer, you mostly just want a lot of miners and picks and a more aquifer-piercing and cavern-claiming focus for survival. A couple of well-armoured military types can help, or at least some coal and ore. Oh, and lots of booze, because it might be a while before you have water (in as few barrels as possible, less vomiting saves on booze). A single pick will still get the job done, but getting a start is more down to luck.
But I just use the default. It saves me having to remember to make everything, and the skills are useful enough, except the Jeweller.