I kept my old 2003 WRX in storage for about 9 months one year as I was back in the UK, and simply disconnected the battery completely. When I came back the only things I had to do was re-program the stereo, and also the electric windows.
Now with the 2016 STI I'd expect a lot more to need to be re-set, but really have no clue. I just looked through the US manual and it mentions the windows needing to be initialised after a battery disconnect, so that's definitely still a thing. Here's an interesting snippet:
Quote:
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It may be difficult to start the engine when the battery has been disconnected and reconnected (for maintenance or other purposes). This difficulty is caused by the electronically controlled throttle’s self-diagnosis function. To overcome it, keep the ignition switch in the “ON” position for approximately 10 seconds before starting the engine.
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Also, don't forget to test your physical key so you know you can get into it - I'm assuming you know where it is and that you'll not be leaving the car unlocked during your time away.
I suppose the ideal way would be to use a battery conditioner that works when the battery is still on the car, that way there's zero loss - they're probably quite expensive for a good one. As it's only a month you could also just leave it connected and gamble it will still be ok (and have a charger on-hand in case it isn't), just make sure to take it on a long run to give the battery a good charge, then park it up.
Oh, and have a good and safe trip.