I'm a Production Coordinator, and I supervise 12-13 shows over 9 months, plus a dance festival of 12-13 companies over three weeks. It sounds like we have a lot in common.
DeeCap has great suggestions - first is to figure out access & policies. Building hours, keys, contact info for other staff. Building tour, tech specs, inventory, hiring & payroll info.
Next, info on your visting companies. You'll need (or need to make) a season schedule of each show, from load in to load out. For each show, you'll want a copy of their contract, their tech rider, contact info, and scripts and/or videos.
Ambrosialx is absolutely correct that you if you coordinate over the phone, back it up with a written summary via email.
After you have the outline of your season, you can start researching each company and breaking down their tech needs: scenery, lighting, projection, sound, wardrobe. Red flag pyro and rigging for immediate followup. Red flag children and animals for when you'll need to stock your liquor cabinet. Joking! Well, kind of joking.
It would be good to know how who your staff is and how they are dividing labor. In my case, my production manager and tech director handle most of this. My duties are much more specific to rehearsal & performance. I would be happy to go into further detail if you find it helpful. I have a before-arrival list, an on-arrival list, and daily detail lists, but these would only be useful after you've gotten a handle on the big picture.
As a stage manager, you will love the challenge of organizing so much information! Dive in and let us know how it goes!
Pro tip: anytime you're getting overwhelmed with all the info, walk around your new building - get lost, find your way back, explore a new corner you hadn't seen before, meet someone and ask them two or three questions about themselves and their job, and ask them to help you with something - directions, advice on how best to settle in to your new job, or where to get lunch. Then, get back to info wrangling. You'll have it all under control faster than you think.
-Colleen