Yes, the poured, floated & sealed afterward slab is the best way to go, if you're up to it, & it's the best anchor. Definitely do at least a 4-inch bed of gravel under everything, this is what moves instead of a slab or blocks or pads.
However, absolutely consult your Building Dept. first & foremost. They have plans for their requirements & you'll need a permit & likely 3 inspections. They have to approve your plan & that approval will hinge on if you can do anymore "paving" on the property, if the shed/coop placement meets setbacks & if the planned structure is sound or even big enough for your vision.
Other than that stuff, going with blocks filled with concrete is pretty solid & much easier. If anchoring the building is done like putting in fence posts then just concrete pads halfway in & halfway out around the perimeter would accomplish the same overall desire & be the easiest by far.
Oh I initially forgot, if the back, friend & truck's good you can possibly use parking lot Wheel Stops (6x6's) for the foundation or more. There shouldn't be any monolithic requirement & they're higher density concrete that's rebarred. It's slightly rednecky, but saves an awful lot of bag hauling, temporary lung damage, form work & drying time...you'll love the pinning holes too.
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This is largely a matter of opinion, but in my experience a 10x12 slab will almost certainly crack. There's no question but that I'd cross-cut it, at least. I might even go so far as to split the length into thirds. Clean, straight lines are preferable to jagged ones, and you can always fill your cuts with caulk to keep the floor surface intact.