Depends on overall design and load, and, in terms of screw/nails, it depends on what will be anchored to what. A floor plan annotated with fastener locations would help.
If you are notching in order to transfer load to the 4x4, a 1/2" deep notch is all that is necessary. Notching will take shear stresses off the associated screws/nails/bolts.
EDIT:
Great new drawing.
The main design considerations are the unit racking and collapsing (side to side), or the units tilting forward and falling over. Attaching the units to the back-wall in a couple places will stabilize the units, particularly their back portions. If the 1/2" OSB is screwed/nailed to the front and to the back 10' 2x6's, then the back-wall attachment will also stabilize the front portions of the units as well. If units can be attached to an end-wall, then attaching to both back and end walls will fully stabilize the units without needing to screw/nail the 1/2" OSB to the 2x6s. If back and/or end wall attachments are not feasible, I'd place 2x4 cleats on the ceiling and secure the 4x4 posts to those cleats.
On both the front and back, I'd put the 10' 2x6s on the inside of the posts, notching the posts 1/2" deep. This will give more support to the 1/2" OSB over the 24" dimension. Another benefit of internal attachment is that the 2x6s will be recessed 3" from the outside edge of the 1/2" OSB and 4x4s. Given that, you'll be able to hang all kinds of small things on the outside face of the front 2x6s without the items sticking out. You could also screw 4.5" wide lengths of 1/2 OSB (or anything similar, such as 1x6) to the underside edge of the 2x6s to create 3" deep shelves for light weight items.
If one end of the unit is open (such as facing the garage door, I'd consider moving the two 4x4 end-posts inward 16-30", which would cantilever the ends of the 10' 2x6s, creating 2-sided open access to the cantilevered portion of shelving.
The 5.5" of space immediately underneath the shelves will be kind-of wasted space. If one end of the unit is open, then I'd attach 24" wide OSB underneath the 2x6s to create deep pockets (cubby holes) open on that one end, for storing long stuff. The 24" long 2x6 end-caps can be under-mounted or top-mounted.
Best Answer
An option would be a keyhole bracket mortised into each side of the shelf. Add screws with drywall anchors and hang.