If you must store hay under a tarp, keep the tarp off the actual hay by stacking pallets on top (watch they don't hit you in the head when you get hay out
) and rigging the tarp so it is not too closely against the sides of the pile.
You just WILL lose a significant amount of hay (ranging from 'some' to 'all') when it's stored outdoors under a tarp, though, so I think you are very smart to be thinking in terms of constructing an actual structure.
If you are very sure of your storage conditions there is no reason not to get a whole year's supply at once; if storage is a little iffier and you are pretty sure you can still get future deliveries (w/r/t availability, price and seasonal condition of the barn driveway, sort of thing) then it is smarter to buy less at a time.
Even if hay is stored indoors, IMHO it is smart to rig a large tarp as a suspended 'tent roof' over it, allowing several feet of clearance between top of hay and tarp, and a good overhang to the sides. That way, if your roof turns out to have leaks or condensate-drips (as many, many roofs do) you will not be farming mold all the way down through the stack of hay.
Good luck, have fun,
Pat