I always end up in decision paralysis because I think of way too many possibilities. Is there a way I can avoid brackets? If I am able to drill into studs should I just use normal wood screws? I'll be using it as a tea/spice shelf.
If those hooks on the top corners are a multiple of 16" apart, and they line up with studs, you could use some 2-3" screws through those into studs.
If they don't line up with studs, you could stain a piece of lumber close to the same color and screw it to the wall through the studs and screw the shelf down to that board. It would act as a ledge for one of the shelves to sit on.
There's no back so there's no easy way to directly screw this shelf to the wall. You'll have to get creative.
You could find the studs and put screws angled through one of the shelves into the studs. Screw from underneath the shelf if it's lower than eye level, above the shelf if it's above eye level. This is so you don't see the screws.
You could get realy fancy and use a pocket hole jig to make nice holes for your angled screws.