How to record your story? Behind the camera

3) what's behind the camera --  director, camera person, shoot/equipment logistics, catering, equipment upkeep, data storage, production notes

This only concerns what is directly behind the camera to make sure the shoot works.  There are other issues like legal and business, but I'll address those independently in the "Who" part of "What, How, Who?".

As part of answering the question "How do I record my story?" you will need to choose a director.  I'm guessing if you are following this blog you intend to be the director whether you also choose to run camera or act in front of the camera (it will almost certainly be one or the other).  On a $4k budget, you will be doing more than one job.  How you and your group split up accountabilities depends on what skills each bring to the table.  And I can assure you on this budget, that group will be small so look for people with lots of skills.

On Holiday, I was director and cinematographer.  That both solved and created its own issues.  Your project may or may not split that way.  I liked it because from a director's POV it was about as close to "pure film making" as you can get -- just me, a camera, and an actor.  I knew my co-producer/actor quite well as thus was able to often anticipate how he would move.  That's always the trick in documentary film making or live sports events: anticipating your subject rather than following it.  Often we did only one take and moved on.  Many of the shots were long takes we knew we would chop up in post later.  So know your lead actor or if you are the lead actor, make sure your DP knows you and can anticipate your choices.

A quick thought on this before I move on: from my experience in making films, both as a director and in working for other directors, choose one person to be the director and don't change.  If you are the one buying, it most likely should be you and you alone.  That is, unless either you have a unique relationship with someone or you know two people who do and they are both willing to take your project on, put yourself in the director's chair.  There have been teams that have been successful, but they are rare, not the norm for a reason and the last thing you want to do is generate additional challenges for yourself.