I have a shed with 24 inch on center studs, anchored to 2x4s on the top. the place where I wanted my open shelves has a 60 inch, single pane window that has 2 inch foam insulation plugging it to keep heat in or out, depending on the season.
Attaching directly to the studs wasn't going to be enough, given the weight and the questionable nails used in the shed's construction.
My solution was to buy some HD, 1x4s and attach them to the top 2x4s and the studs, as well as to the window framing where possible. If you add insulation and dry wall, this will also work to reinforce the shelf mounts. I use screws to mount things like this so I can change my mind later.
I think that if you are storing really heavy stuff on those shelves, that you will want to reinforce the connection of the studs to the joists with metal straight or angle brackets
I just used simple metal sheving brackets since the shelves are not that deep. Another option would be to mount the long brackets with movable shelf brackets (found where they display the wire shelving systems), but they can interfere with storage since the brackets can be up to 3 inches high. The advantage is that you can re-space your shelves, although I bet you never will once you set it up.
French cleats are neat, but you'll have to make a lot of fitted parts to hang stuff up. Make sure you always cut cleats' mating surfaces to the same angle!
Here's two pictures of the open shelving in my little shop. I don't keep tool cases on the shelves since I have another place for those. The first picture is of the wire shelf construction 18 inches deep. The second picture is the 1x4 I described, which has a max depth of 12 inches. The top 3 shelves are just 9 inches deep.
The more I do, the less I accomplish.