Elmers glue is one of the best wood glues. One of the wood working mags did a very good test a year or two ago. The tested all the high dollar "modern" glues and Elmers yellow wood glue out performed most on most tests. It by far was the best bang for the buck.
If you want to go overkill get a block of wood over twice the thickness you require. Then saw it in half and plane to thickness. The saw cut sides will match very close when sanded when oriented like you opened the block up like a book. For best strength for edge to edge joints, route a tung and grove in the mating surfaces and then mark and drill either pin holes or biscuit slots.
A bit easier is to square up edges to be glued, drill holes for cross pins, BRUSH the glue on both surfaces and pins. Drop a little more glue into the holes. Push pins in and bring boards together. Clamp boards together tight. Wipe excess glue off with a damp rag and let set over night. If you miss a bit of glue you can get it when you sand the boards down to final finish.
