A month is essentially nothing - in terms of storage in a garage.
I believe a lead-acid storage battery loses something like 10% of its charge per month. Naturally you will lose more running the on-board equipment. When you get back, put a charger on it and you'll be all set.
Currently I drive one car in the summer and another in the winter. I don't let the off-season one sit the whole time, but they do sit as much as a month anytime.
The more fuel you have in the tank the less it will degrade overall - because there is less interaction with air.
Enjoy your trip, knowing that your car is safely parked inside!