Depends on what you want to do. If you construct the guitar in such a way that you could one day do a neck reset, the cold glue is the one for the neck join. Otherwise, you could use the water resistant one as well. I would if finishing the guitar with oil to prevent the glue accepting humidity over time, but I normally stick to cold glue.

Yeah, the cold glue definitely. Very strong, but can be separated during repairs with a hot feeler-gauge (or similar, if necessary). Go for the Alcolin Professional, not the white glue, as it sands much better! :? My 5pence only.

Titebond or Hide glue for neck joins.