The animals that you can bring with you at embark are determined by what your parent civilization has access to. Usually this is limited to the common domestic animals and tamable wildlife, but if you turned exotic animals off ... any creature they come in contact with is potentially tamable. Giant cave spiders and other subterranean wildlife is normal to find in this way since the underground is everywhere and your civ will have found them. The other animals will depend on the location of your mountainhome (if its in a jungle, you will see jungle animals). The same logic applies to plants, trees, ores, and other materials. So if for some reason your mountainhome has no iron, you won't be able to bring an iron anvil or any iron tools (how they are then able to make steel is a different story...)
Personally, I don't like playing with exotics off since immigrants can come in with any of those creatures as pets. So even if you just wanted to be able to tame everything no hassle, but not cheatyface your way into overpowered pets, you can't. Had an immigrant show up with a gremlin child as a pet. That gremlin decided it was going to be a hunter, grabbed a crossbow and roamed about outside. One day it shot down a forest titan. Which was awesome and all, but I felt cheated out of doing it myself with my own military.