You don't mention the thickness of the card. Thinner stock will be more likely to warp. Regardless, my solution, where glue choice is concerned, would be to use PVA based glues. This can just mean many of the commercial white glues (Just not the ones necessarily marketed to kids or the inexpensive ones). They are good for paper crafts and are economical so can be an easy go to. They can also be forgiving for mistakes because you can just use some soap and water to clean them.
If you have some available some other choices would be cement glue or even something simple like Mod Podge. Careful that the former is vented properly during application before and after (it stinks). The ladder might not hold the test of time depending how you use it but I have plenty of crafting projects still holding up for several years now.
As far as making sure it does not warp I would suggest using an acrylic spray on both sides of the card. Let that dry before you apply it to the book. That should discourage warping and seepage if the glue ends up being too concentrated in one area.
With all things like this I would encourage you to test it out before doing something you might not be able to undo.