How do I design a shed to make optimal use of building materials?
Most builders never even consider this and just create a building large enough that some waste can be reused (e.g. small pieces of drywall in a closet or a bad piece of lumber as a cripple below a window) while most waste is just tossed.

For something you build yourself, start with the outside measurements and get those on an even measurement. Consider how the wood sheathing will overlap on the outside, so an 8' span of 1/2" material can actually cover 8' 1/2" since one corner will have the next piece overlapping the end. Don't worry about cutting an inch or so off the floor, since as you say, you're better off removing material than cutting a patch from a larger piece. Studs come in standard heights, so just use that height.

When it comes to picking the thickness of lumber, I'm a firm believer in overbuilding the floor of the shed. It costs a lot less to overbuild this today than to rip things apart because the joists have weathered poorly. For the rest of it, I suggest leaving it exposed as a shed. The ceiling joists make a great storage space, and it's nice to nail things on the walls, so interior finishing of a shed is a waste of material IMO.

For things like siding, doors, or other less generic materials, see if the local Habitat ReStore has anything useful in stock. Most of these are waste products from a contractor that bought too much or the wrong style, so you get to help a charity and keep things out of a landfill at the same time.