What conditions should a company commander establish within their first 30 days?

I agree with MAJ Guy....the first thirty days are pretty much evaluation...you need to know what your Company is, what it is capable of and how your subordinates react to each other...also give yourself the opportunity to welcome what's good and what can be improved from the standpoint of your PLT Ldrs and NCO's....this is the time where trust is developed, your troops get to know you and you get to know them.....inform your higher what your initial plans are and ask for and respect his/her guidance....

unit priorities, commander's expectations, current command climate, and an agenda from a professional and family environment

You need to establish your vision and expectations from the lowest level to your level. Then assess your unit before making sweeping changes. Sometimes there are things that don't need to be reinvented. Wastes energy.