Can you provide a sketch or photo of what you have? It sounds like you want mortise and tenon rather than a dado. You are looking for a strong joint with a nice clean appearance? It is also possible you want a sliding dovetail joint. Without a clearer image of what you are trying to do it's tough to give the right answer. Are these 1 x 3"s the top and bottom? If so you might save a bunch of work by using Miller dowels. The Miller dowel system uses a special stepped drill bit which is progressively smaller towards the end. You simply drill and insert a Miller dowel with glue on it. Tap it firmly in place and remove the excess dowel. Two of these per joint would be plenty strong. View them here: http://www.millerdowel.com/