Favorite glue, the only glue that does the job for me anyway: Neutral pH Adhesive, archival quality by LINECO. It is "permanent, dries clear and remains flexible".
I love YES! paste. It doesn't make paper buckle and, if it dries up, you can spritz on water and it comes back to life.
Golden GAC 100 has been my preferred glue for most circumstances for about 20 years.
I also use the Golden Gel pastes for things that are heavier and need a stronger bond.
Sometimes I use a spray glue, Elmers does a good one available in U.S.
Recently I started using a specialty paste-like glue that is from Japan and made specific for origami paper (Yamato Nori Rice sticking paste). It can be found in shops that specialize in origami paper and supplies - which I realize outside of Japan or San Francisco and Los Angeles, might be harder to find.
Currently I am in Mexico where I just finished a large scale art piece, I ran out of GAC 100 and had to supplement it with a local glue. I liked it so much, I am taking an extra bottle home to SF. It's like a heavy-duty version of Elmers - Pegamento Resistol 850.
Thank you for the Golden GAC 100 recommendation! I can't wait to try some.
This guy uses it on Cartón Board: https://www.youtube.com/watch?v=rVSLFK2MNpE
i use elmers 2 part and one part wood glue, the way I figure paper was wood so it should hold. I send naked mailart in the form of postcards daily. I Have very rarely have comments about condition of the cards received.