The quickest, most reliable adhesives I know of are epoxies... they're always two parts which you mix together just before gluing, most are waterproof, and they set in a specific time. They're made in all sorts of hardening times - 1, 3, 5 and 10 minutes after you start mixing, or, for higher strength, up to 24 hours like JB weld (which works wonders on anything, believe-you-me).
Mix it together after you've got a lot of parts cut and set up, then use a toothpick to apply glue to very small pieces. It's usually very, very sticky until it sets, and will adhere alomst anything, especially if the surface is rough...
If what you're using is wood or paper, you might try a polyurethane glue like gorilla glue, but it's usally brown and you'll have to be more careful about messes, and poly glues require moisture to set. Epoxy is often clear, especially the quick set kinds, and doesn't shrink after dry. Another great, clear adhesive is silicone aquarium glue - Its set time is a bit longer (half a day?) but it makes for a nice, flexible bond which will even stick to smooth glass
All this at your local hardware store...
(and I'm serious about JB fixing ANYTHING)