What is it you are looking for:
Inexpensive.
Low maitenence.
Good looking.
A closed in area, all 4 sides, or an open lean to, only a roof, or 2 walls but open on one side.
Do you want door(s) inthe narrow ends of the leanto, or along the 32 foot wall of the leanto?
Are you most concerned with cubic feet to store hay (taller would allow it to be smaller) or do you need square foot floor space (to park machinery).
What is the wall of your current barn, metal, wood, concrete, pole.
You are getting a wide range of ideas, perhaps narrowing down what you need and have will help get a general direction that works best.
Myself, I dislike flat roofs, I dislike the membrane coating, I really really like steel metal roofs like you do. I have a very healthy snow load 'here' so I tend to like a good roof pitch. I just couldn't imagine those flat things others picture, we get snow starting in November sometimes October, & none of it melts until March or more likely April. I like laminated posts, not a 4x6 or 6x6 as wood these days is poor and crooked, a laminated one of several 2x6s is much stronger & you can treat only the parts that are in the ground, not the whole thing.
Where do you want to go?
--->Paul