Are you literally using toothpicks or are you building a stick and tissue fusilage with balsa, spruce, or basswood strips that resemble toothpicks?

CA is the most popular glue. "CA" is short for cyanoacrylate glue. It is also known as "Superglue" which should always be capitalized because it's a registered trademark. It comes in different viscosities. Super thin, which runs like water, will wick into already assembled well fitted joints and then cures in mere seconds. Medium, which is slightly thicker, can be used like the thin stuff but is more forgiving and fills gaps in the joint better. It also takes longer to cure. And then there is the thick CA, it's like syrup and can be used like normal glue, wet the wood first and then assemble. It takes the longest to cure. The cure can be accelerated by a spray on accelerator like "Zip Kicker". It has strong fumes and some people are allergic to it.

Some people prefer wood glue like Elmer's Carpenter's wood glue or WeldWood. You can get this glue from your local Home Depot or Lowes. These glue joints need to be clamped or pinned securely until the glue is dried. This glue is stronger than the wood you are gluing together and it sands really well. Accidental spills clean up with water. There is almost no odor and hardly anyone is allergic to it.

And then there's epoxy. Really strong (overkill for balsa) but also heavy. Good choice for plywood firewalls. Epoxy also resists fuel and almost all other known chemicals. Some people are allergic to it.