I have "student" bookcases I built years ago, which have 4'-long 1x12 (nominal) shelves supported only be a pair of shelf clips at each end, carrying two solid rows of paperbacks each. (One upright, one tilted back in front of them.) These sag just a bit in the middle, but have no trouble handling the distributed weight.
You've got a shorter span, so you don't need the stiffness of my 1x12s. And if you're using shelf brackets at the 1/4 and 3/4 locations, the weight "outboard" of the brackets will tend to balance the weight between them, so sag would be less significant (and better distributed so less visible).
So I think the real question here is only how well you can affix the brackets to that wall.