The thickness of the sheathing materials you must use is written down on your building plan. If it says 1/2 inch plywood, then you have to use 1/2 inch thick sheets.
What should you use? Now here you do have a choice.
Plywood or OSB (oriented strand board) sheathing, it makes very little difference on which to use. I used plywood sheathing for the sub-floor for the longest time, but OSB sheathing has improved, and you can use it as a substitute for plywood floor sheathing. On a wall there is no problem and either will do the job. Just make sure that you get good quality sheets.
Minimum thickness of wall sheathing for use on walls; 3/8" plywood or 5/16" OSB. If you use fibre cement siding, go with 1/2" plywood or 7/16" OSB for the exterior walls. The wall sheathing can be nailed or stapled (check your local building code). Use 3-inch spacing, 16 nails or staples for the edge rows and a 6-inch spacing of the fasteners for the inside rows, nine nails or staples. This may seem a bit excessive, but this makes for a strong home, able to withstand most of the forces that nature throws at you.
In addition to fastening the sheathing into the studs, add two nails or staples in the top and bottom plates between the stud spacing.
These nails placed in the plates between the studs will do more than the other nails, they make for a strong wall that will keep the building plumb. That is, assuming that you levelled or squared your wall properly before fastening the sheathing.
The minimum thickness to use for roof sheathing is 7/16" OSB or 1/2" plywood for rafters and trusses 16 and 24 inches O.C.
Roof sheathing can be nailed or stapled.
Nail or staple sheets with 6-inch spacing for the inside rows and 3-inch spacing for the edge rows. And use three nails or staples in the sub fascia and ridge blocking in between the trusses.
2 1/4-inch box or common nails or 2 inch gun nails (the spiral ones are excellent), 7/16" crown 1-3/4" Leg, 15 Ga staples.
Using staples to fasten plywood is not allowed in all regions. Check your local building code before you start.
As a plus staples are much cheaper than nails, and if you use the right size compressor, much faster to apply than nails. The one negative thing to say about using staples, very messy if you have to take things apart, if you need to change things.