I'm not an expert, but I beleive wood is easier to split green. Anyway, for my smoke wood - I always chunk first and put in garage - in a container, off the ground. Whatever you do the key is to keep relatively dry and off the ground, with some airflow. Insects and mold are the biggest problems in my opinion.
I have a peach tree that I occasionally get a limp or two from. I lay it under the the cedar trees out by the wood stack (used for the fire pit) away from the house and cut chucks as needed. I let it sit for about a year befor I start using it to let it dry out a bit. As metioned, plenty of air and keep the bugs away from the house are the keys.
As long as you have good air flow you shouldn't have to worry about mold just don't cut it into chunks and then store it in a plastic container with a lid on it.
I just got gifted some short sections of pear wood. I intend the cut it into chunks and store in a plastic milk crate (you know, the kind with lattice sides). That should allow plenty of air circulation and keep it at the ready: