I've been storing cars for 25 years. One month can drain your battery...keep it disconnected until you get back. I don't think one month will affect the fuel significantly. I've driven on 6-month old fuel! Though I agree with G-Benz. He's saying that rather than keeping the tank full, you may want to keep it near empty. That way you can fill up with fresh fuel when you come back.
95 E320 Cabriolet, 131K