democracy, there is no 'which to build first rule', and only you can decide for yourself what shelter works best for you. myself i like a tarp shelter, ive tried debris huts, not to shabby but i still have better luck with the tarp. cheap 8x10 tarps can be found for as little as 4 bucks. if you carry a small bit of firestarter with you it wont matter how wet the wood is, but practice at home first. i carry some fatwood sticks, small ones that dont take any space, and a couple of weber firestarter cubes. along with my
firesteel i can get a fire going almost anywhere. myself, depending on the conditions(raining, snowing, dark already), i usually prefer to get a shelter built(doesnt take as long with a tarp setup as it would building from foraged materials) and then gather as much wood as i can find. dead evergreen boughs burn well even if completly saturated with water because of their resiny properties.
like i said it all depends on you, the area you are in, what you have to work with, and most of all, being prepared.
im not sure if you are trying to do the les stroud or bear grylls thing, but in my opinion what those shows are for is mainly to try and show you what to do if you are put in that situation. real survivalist/preppers survive by being prepared for the worst, or at least having what is needed to get through the worst. i would never go into the woods without 2 ways to make fire, something to be used as a shelter(tarp/hikers tent/something), and a good light/headlight to see to gather wood for fire. and a way to purify water for drinking/cooking after the supply i brought in with me is depleted.