The best glue? you are asking for tons of responses from people full of opinions ;)
I've had a lot of luck and heard other people have as well with Gorilla Glue. Go to the woodlinks section at this site, click on the glue section and look through that.
One small warning.... do not use gorilla glue at 11:00 at night. I did. It's the consistency of honey and has no known solvent. I didn't realize I had a little on my face until I woke-up the next morning. :)
All of todays glues are stronger than the wood itself when properly applied and cured. For your use stated Yellow wood glue would be the choice I would make. It it is going to take you a while to get the pieces glued together and clamped the elmers white glue allows for more fuss time than the yellow pva glue.
The only time you need to do anything else is if you have a waterproff application Gorella glue. Or you are restoring an old piece and then I would go hide glue.
I use yellow carpenters glue (tite bond) for everything ecxept box and dovetail joints i use gorilla , good lucck and dont try to clamp so hard the glues squeezes out it makes the joint less strong, and i always leave the loints clamped up for about 1 hour and ake them off then ill leave it alone for a bout 24 .
Good advice Jeff
The major cause of glue failure usually stems from the natural instinct to clamp the living daylights out of it and leave it in the clamps overnight. Both, as jeff states, weaken rather than strengthen the joint.
Without giving you a long and boring dissertation on the principles of adhesion(mechanical vs.specific).
Basically once the glue has given up some of its water by absorption It still has enough flexibility to hold the tension that any stress in the wood is still imposing and cure appropriately.
God my brain's fried and I can't explain it clearly.
If all else fails, as they say, read the instructions. I think you'll find that on most containers they give you a recommended clamping time.
I know my Titebond bottle does.
Cheers one shagged out Limey