Having experimented with hay storage for about ten years now, I can definitely tell you what
doesn't work, lol.
John, are you growing and storing your own hay? Or purchasing it already baled? The concern for fires is with still green uncured, partially cured, or wet hay. If that's the case, then a separate shed would be your safest bet (only second to properly drying it before storing). Depending on your climate conditions, I would recommend not placing the bales or stacks directly on the ground. I've found that even when it seems dry, the bottoms of those bales or stacks that are in contact with the ground are the first to decompose. I've lost a lot of hay that way.
Pallets work well because they get it off the ground and allow some air circulation under the hay.
That being said, when we built my dream barn we included a hayloft over the goats, with a hay chute to drop hay directly into the hay feeder. Although there are some challenges getting the hay into the loft, it's wonderful to not have to wade through a pack of grabby goats with the hay in hand. We both buy hay and grow it. I just make sure the homegrown hay is completely cured.
That was for my convenience, I admit, but I agree that one can never have too much storage space.