Congrats on your new position, Jon. I am not a Maintenance person, but I manage and have managed many. I am happy to see you are asking about reading books - I would suggest looking into any of the online training courses your company offers (The Training Factor/Grace Hill) and getting your EPA certification. That's as far as my knowledge goes there.
Organizing a shop though is dfferent. Have lots of bins labeled that fit on shelves in your Shop. Divide area into: Plumbing, Electrical, HVAC, Painting/Prep, Tools (nice to have hanging pegboards on the wall over a tool bench), Windows (balances, blinds, etc., and a couple of Buckets ready where you keep all the stuff you need when you are going on a service call or when you are working in a turn unit. Because I believe in inventory lists, in each "department" you can keep a list of stock. As you use items, you can cross off so you always know at a glance when to place orders. In another area, you will keep chemicals. You need a notebook that contains the Safety Sheets (MSDS but they stopped calling them that.) These safety sheets list all the chemicals in a product, what to do if swallowed or gets in your eye and has to be a certain way according to OSHA. If you are not familiar with this, you need to get trained. This area contains your PPE gear (eyewear, gloves, masks, etc.)
There will also be a place to store rakes, ladders, snow blowers, your golf cart and all that.
You probably have a lock station with key machine and everything that goes along with that.
You should have a computer with the software to log in completed work orders. Then there are file cabinets - every Shop is different in what they keep there versus the Leasing Office in the way of warranties and manuals.
I find that a lot of maintenance techs and supervisors are really the ones to educate the Managers and Leasing teams on the turnover/make ready completion process. I thank God for them everyday. So, you may need to gently help your other team members.