I personally wouldn't focus too heavily on miners, since you'll be using pre-mined space for a lot of things. You could also bring a bunch of ore and whatnot and erect a quick wall around your wagon (preferably with a roof) so you don't have to be forced to quickly haul stuff down to the caverns.
These are the steps I'd take for a rapid cavern fort in a hostile embark:
1. Ice hole. Small room just under the surface, get everything living below the surface so that even if wildlife wanders close to the wagon, they won't see any fresh dwarf meat to murder. This also gives you room for a mason's shop and a bit of ice to make a wall around your wagon if you don't want to bring materials. You could dump things underground instead of making a wall around the wagon, but if you've brought ore it will be faster to just make a quick wall.
2. Find caverns, probably with roadar.
3. Send a group of your starters out in a squad to scout the caverns, reveal stuff, and find good choke points to seal off. A pair of dwarves should suffice.
4. Since you'll only be dealing with the first cavern level and have 5k points, you could bring equipment or forge stuff on-site while your miners are digging down to the caverns; fighting to secure a portion for yourself will be viable in the short term. Digging a staging area pre-cavern breach could give you the stone for blocks you'll need and time to make said blocks and equipment. A pair of trained fighters should be enough, or you could draft your miners and make them do the scouting. You might want them for other mining purposes while scouting, though, and it never hurts to have more pre-trained dwarves in a hostile land, so.
5. Wall off the choke points ASAP. Eventually you'll want to secure the entire edge, but for now you just need a hunk of cave to call home. Your scouts can stay on guard duty while your mason churns out blocks and everybody else moves them into place. Drafting the miners remains an option if your section of cavern will be difficult to claim.
6. [regular fort stuff, except your farm plot is in cavern soil for now]
7. With a basic fort setup and a hunk of the caverns taken for yourself, congrats. If your biome is reanimating, your new top priority is not letting undead take over any of the caverns and destroy your FPS. If you're brave and have no water on the edge of your first layer, you can probably capture the entire first cavern for your own use so that your fort is able to grow over a larger area. Otherwise, you'll have to capture it bit by bit, which will be slow and dangerous if your embark is large.
Also... don't bring animals. Cats and maybe sheep if you're worried about not having reliable caravans for wool cloth, but you will not have a thriving meat industry if your embark is reanimating. Do not pit your pack animals, just butcher them. That way you won't get a terrifying zombie bull trapped in a pit, and will instead just have free meat and, at worst, a hair that will get instantly kicked to death. Just tan and spin the stuff quickly so your dwarves don't get spooked.
I also disagree with the advice of bone armor and wooden weapons. Your dwarves' time is valuable right out the gate, and even with metal weaponry you should be wary of sending them into combat repeatedly lest wounds accumulate. If you don't have time to forge metal weapons then your miners are your best line of defense and a dwarf with a wooden axe isn't going to change anything. I guess you could do obsidian short swords if you really want to, since they're quite effective on unarmored creatures and don't take any longer to make than a wood axe.