Less expensive 1 3rd less board footage of lumber fewer pieces to handle fewer joist hangers to have to attach and only one half as many screws to attach the roof steel.
Ok to use 2 x 4 for for roof rafters.
The back of the roof will attach to house with 16 2x4 and lag screws.
Somehow i am in a traditionalist camp 16 oc for a 12 foot wall will add only 6 extra 2x4 s or 3 extra if you buy 10 foot lengths for the rafters and 6 extra 2x4 s for studs if you use only a single layer top plate on the bearing walls.
An syp rafter can span 11.
As mentioned above a 2 4 spf shed roof rafter can span 11.
At the pitch range you are looking at the 2x4 is just fine up to 8 6 depending on the lumber grade.
Rafters to 2x4 with joist hangers.
Both of these are for light roof loads.
The secret word is truss.
Makes construction easier too.
I think you will be fine with 2x4s so long as they are closer than 48 apart.
Structures such as sheds or barns can be frames with rafters every 24 again make sure to consult local codes.
If your project had a rafter length of 8 or less a safe and strong method is to use 2x8 framed 16 on center.
It is always better to have a large rafter rather than be concerned with a sagging roof.
Also if you want to make things cheaper you can do a single slope of the roof and basically cut out the eve cost.
Rather than having 2 4 purlins every 12 it would make far more sense economically to use 2 6 purlins every 24.
You can use them for roof floor and even wall framing but few sheds will need trusses for walls.