7 16 will be fine for 16 on center and 5 8 for 24 on center rafters.
Osb for shed roof.
For the curious 7 16 osb has a span rating of 24 16 and with supports every 24 inches is good for a roof live load of 40 psf pounds per square foot with a 10 psf dead load.
Standard asphalt shingles do an excellent job keeping the weather out.
Plywood with similar propertiescurrently costs about 30 more for an equivalent thickness.
Underneath the shingles is osb sheathing.
However moisture has a way of finding its way into a structure.
Thicknesses range from 5 16 to 3 4 inch and the proper one to use.
Sheets of 7 16 inch thick with no edge support can be used in an area where the snow load is 30 pounds per square foot.
This is a type of engineered particleboard made specifically for covering the roof of a shed or dwelling.
The thickness required by josh s circumstances are good for roof snow loads of up to 70 psf again spanning 24.
Using oriented strand board osb for shed walls floors and roofs.
Osb comes in 4 by 8 foot sheets as does plywood but the manufacturing process allows the production of longer and wider ones.
With edge support and the same snow load 3 8 inch osb can be used.
Osb is fine all the way around.
Using oriented strand board is a tested way of reducing costs for building your shed.
Good enough for houses good enough for a shed.