For this, cutting sheets of material like plywood or MDF, I recommend a downcut bit.
The bit presses down as it cuts (as opposed to lifting up as standard drills and end mills do) This will help prevent the little tares that are common when cutting plywood, or the chipping that occurs when cutting MDF.
My 1/4" downcut from the local hardware store bit is my most used bit. 
However, to do dovetails like in the picture you have to add “dogbones” to the inside corners. These are a little extra cuts to allow the corner of the matching part to fit. As a round bit can’t cut a square hole.
The smaller the bit, the less extra space made by the dogbone. So a 1/8" downcut bit is nice for this.
Here is an example: Continuing the discussion from Tiki Dice Tower