glue choice
For wood joints, I'd say an aliphatic resin glue, like the original TiteBond, is fine. Clamp time will be a hour or so.
You'll find a technical PDF on their website, if you need guidance.
I wouldn't get carried away... you don't need waterproof glue and the polyurethane glues are a pain, if you need to clean up the joint after clamping.
Good Luck