Congrats Dawg Well Done.

I am so jealous. (This poverty stuff is not for the squeamish.)
A water well IS at the top of anyone's list But may I offer a few ideas of my own?
IF, as you say, not many would see it ... what about a locking gate so that the wandering local youth with friends looking for a "safe place to drink and shoot tincans" (for just one example) won't accidentally stumble upon your gulch? ("Hey look an abandoned shack ...I wonder what's in it?")
How about buying a used travel trailer as a first domicile which would allow comfortable living while in the process of building the gulch proper? Not reccommended for permanent usage in the
winter unless additional insulation (
hay straw bales stacked around it?) is available.
A used shipping container as temporary "safe storage" and possible first barn/buried retreat?
I do not own land myself but do own my own mobile home, currently located in a rural trailer park outside of a small rural town. Not a perfect situation but comfortable for now. Largest town over 20 K is 65 miles away, still not far enough but doable so far.
I know that many here will
boo and hiss at this one But what about a short "Howdy Do?" with the local Sheriff so that he is aware of who the owner actually is and that you are Not the lead element of some tear wrist group moving into the County he is responsible for. This will also give you a good chance to evaluate the man and his "political" leanings. If they are totally statist then you are at minimum warned ahead of time.
If he is not, most western states rural Sheriff's are not statist, IMHO, or not completely then that also is a good info byte. Some of them are very "Good Ol' Boy" oriented which is very similar to statist in my opinion. Still good to know ahead of time. No?
Here again my humble opinion, most country folks are happy to not have any Outside government in their lives if at all possible. The Sheriffs from these areas are of the same cloth.
Just random thoughts ... take or leave what you will.

Again Congrats on the land purchase.