For my second cigar box guitar, I bought a six foot length of 1 x 2 oak from Home Depot. I made sure the piece of lumber was flat and straight. It weighed a lot more than the pine wood I'd used in my first cigar box guitar, and felt a lot better in my hands. I also bought a small metal miter box from a hobby store to cut the fret slots in the neck. This time, I made perfectly straight fret cuts.
I shaved off the part of the neck that attached to the cigar box so that the surface of the fret board was flush with the top of the cigar box, unlike on my first cigar box guitar. Remembering Mister Jalopy's dictum, "screws not glues," I screwed the neck to the cigar box with three fasteners. This way, if I need to make changes or later want to swap in a new cigar box, it will be a simple matter to remove the screws.
I made a couple of small mistakes, like drilling a hole in a spot that hit a screw going in a perpendicular direction to the hole, but this guitar build went very smoothly. The action is low, but not so low that it buzzes, and I can play the strings all the way up to the highest fret (the 20th) without interference.