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If you go with screws and glue, predilling is going to be a must, the mdf will want to split otherwise. I too like the rabbetted and dado construction, but as Bossnass says it is much more complex. keep in mind that no matter what type of construction method you use, the glue is what is going to hold it together.
As far as building it in sections, the shorter the horizontal spans are, the less you have to worry about sagging, so the three tall units are the way I'd go.
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