What do you use for gluing parts of cards together? What do you think is best in terms of strength, manageability, and invisibility on drying?

I use regular superglue, don't put too much though or it becomes too stiff and will snap. I doubt this is by any means the best option, just what I am using currently.

I use this for gaffs that are taken from and added to the deck in pockets etc and they are mostly very good if it is done correctly when making them. They become slightly less bendy but that is just due to the fact of having parts of various cards together.

This should work for what I want. I like super glue I just wasnt sure how well it holds up to "peeling".

Its a ;little tiny addition to the card. (For Tunnel Vision, if you know the effect.)

I use Uhu glue sticks as suggested by some folks from England for crafting modified card creations.
Works very well. so far it seems to meet the criteria you mentioned for me.

for manageability - rubber cement

Yeah for that bit of what you mentioned I used I few drops of superglue, it's really stuck!

the brand I used is Loctite superglue (think that's just regular superglue) it's the type that a few drops on your fingers will stick them together

I've also used superglue for larger additions to cards and it works well. Had a slight problem with a different piece of card being stuck to a playing card but I think I used glue in the wrong places and it works now

If the area is large enough, I'll use Super 77 spray glue by 3M.