Throughout the following I'm imagining the 'ledge' piece is attached to the top edge of the back, leaving only the joint between 'shelf' and back to worry about.
Given the relatively low strength requirement here a glue-only butt joint might actually be sufficient for this, remembering that well-made glue joints are literally stronger than wood. With modern plywood there is unfortunately a potential doubt about how strong the surface veneer is and how well it's attached to the next ply1.
The glue-only option is easily testbedded using a couple of scraps of the ply you intend to use and seeing what it takes to break it apart. However, nails or screws, or dowels, through the back into the edge of the shelf add significant reinforcement and take little to no effort so I see no reason not to do one of these. Screws would be the strongest and most secure (since each one acts like a little clamp, pulling the second piece of wood into the first), but arguably the weakest (nails/brads) aren't exactly weak if done right2.
Another reinforcement option is a glue 'block' underneath, running the full width of the shelf.
If you wanted to overbuild the heck out of this, not for peace of mind (don't think it's necessary) but for practice, or the challenge of building it, you could house the edge of the bottom shelf into the vertical piece (option 1 here). Although the groove would most commonly be done using table saw or router these days, it could be done with handtools only if necessary. Alternatively if the back is built up from strips of thinner material the housings could be left behind in the construction; a very simple option for the TS owner.
1 Build from solid wood on the other hand and this worry goes away, and the security of the glue joint becomes a virtual certainty. Even white pine would be perfectly
2 Using more of them or dovetailing for mechanical advantage; but really, both. Since brads or nails are so cheap it makes no sense to skimp on them, and the only reason not to use dovetail nailing is if you want the pieces to be more easily separable.