There are some basic applications for joining wood pieces together like these:
In your case, you have horizontals (the shelves) joining to verticals (the posts). It's best not to rely on fasteners to support the loads which are pressing downward, rather use the joint itself, like a dado, mortise and tenon, or dowels rather than a butt joint.
That becomes an issue if you don't have the skill or patience or tooling to make the joint. Dowels are some of the easiest to make, needing only a drill. Mortise and tenons can best be done with sharp, sturdy chisels (somewhat expensive) made for the purpose. Dados can be done by hand with a special plane (rather rare) or on the table saw or a radial arm saw with a dado set.
If you can't dado the shelves, it's best to use a support cleat, bracket or shelving pins drilled into the posts for support. If the shelves are fixed at their location, the case will be more resistant to "racking" when pushed sideways. When loaded with heavy weights, books or records, racking is a big issue and puts a lot of stress on the joinery. Dados are most resistant to racking if glued and made properly.
To understand racking, imagine a cardboard box with all the flaps folded flat into the rectangle. It's not very resistant to pressure applied sideways and will collapse easily. Now fold the flaps on the back out, and tape them in place to form a hollow rectangular shape. It becomes quite sturdy and resists sideways pressure. The result is much like your design concept, an open construction.
A backing piece helps resist racking when the shelves are glued and nailed in place, the most common method of construction. Your design resembles two vertical ladders separated by the shelves with a back attached. The shelves can be supported using "notches" in the interior corners of the posts, like dados only "stopped". (See the diagram above) If the shelves are made with several boards glued together that will be best for strength. Loose boards won't have much strength.
A sketch of the complete design showing the shelves location and
will help us to give more specific advice and will help you to understand the construction and joinery needed..... :smile3: