Assuming that "station" means a structure (rather than "stop") maybe the smallest enclosed station is in Ticonderoga, NY and the smallest unenclosed station might be in Port Kent, NY. Both on the route of the Adirondack.
I'm pretty sure that station means any place that a scheduled Amtrak train will stop on a regular route. Bus stops are kind of a different thing since all it takes is a sign on a post, which may even serve another purpose. I'm thinking there's got to be one somewhere without more than maybe one concrete pad and a signpost.
Quite a few have fairly long platforms, even if they're kind of old asphalt deals or ones that are well worn. I mentioned coming across the Berkeley station for the first time and seeing nothing more than a sign on a post and a bus stop style bench.
Someone mentioned Elko. Doesn't it sort of look like the entrance to a prison, with the shelters looking like guard stations? The chain link fences might be a bit short though, and no razor wire.