I'll chime in because I've tried most of these setups in a series of prewar kitchens. Storing an empty, dry half-sheet in the oven is not dangerous by itself, but the failure mode is real: you're running late, preheat, then smell hot metal/old oil and either burn yourself or panic mid-recipe. I keep a small rubber band on the oven handle as a visual cue if I ever store a pan in there — ugly but effective.
big_city_beth, your cabinet above the fridge works only if you can dedicate that shelf to pans and stand them upright. If you're renting and can't drill, look for an over-the-cabinet-door rack (same idea as a pantry basket) and use zip ties if the hooks are loose. For my current kitchen, I have a narrow wire rack on the countertop behind my dish drainer that holds a quarter-sheet, a half-sheet, and two cutting boards vertically. It's not pretty, but it's better than lifting foil-lined pans out of a cabinet.
One caveat: if you store pans under the sink or near steam, they will pick up rust/smell faster, especially if they're cheap uncoated aluminum. RiverdaleRambler is right about magnetic hooks — only some pans are magnetic, and magnets strong enough for a half-sheet can scratch cabinet paint if they slide. If you use the half-sheet multiple times a week, keep it. But if it's an occasional pan, a quarter-sheet and an 8x8 cover a lot of the same ground.