I assume you want to span the narrow direction.
If so, 2x4's for the rafters will be fine.
If you don't put a lot of heavy stuff in the attic space, 2x4.s will be OK there too. This is especially true if the ceiling is open or not dry-walled and finished.
My 8x12 has 2x6's because I wanted to be able to go up there and load it with heavy stuff.
I do advise a 12/12 pitch, if the height doesn't exceed zoning requirements. This gives a good storage space. I framed out a 4x4 hatch into the attic. You could also add gable end doors for access to the attic from outside.
A gambrel roof will give the maximum attic volume.
3 tab shingles are the lightest if you use lighter roof framing.
Continuous ridge and eave venting is a must.
If you are in high wind areas, use metal straps to tie rafters and joists to wall top plates and studs, and studs to sill plates. Use anchor bolts at 4'o.c. to anchor the sill plate and sill seal for a moisture barrier.
I recommend a double top plate and house wrap.
An overhang is needed for the soffit vent and to keep rain off the walls. An alternate to the closed soffit is exposed rafter tails. But then you need a way to keep critters out and still have ventilation.
On a structure this small, a ridge beam, as opposed to a ridge board, is only really useful if you need load carrying capacity for something like a hoist, or want to keep the ceiling more open. If you do count on a ridge beam, you must have supports that carry the loads down through the gable ends and end walls. If you have openings in the gable ends or end walls, you will need adequately sized headers to transfer the loads laterally around these openings.
I recommend sheeting the whole roof with 30# felt or the new composite felt material. If you heat the space, use ice and water shield at the eaves.
Install drip edge at eave and rake.
If using a concrete slab, make sure it is high enough above surrounding grade for positive drainage away from the structure.
That's all I know...
Bill