What glue should I use with acrylic and transparencies?
There are specific glues manufactured for gluing clear and colored acrylic. It is thinner than water and will spread via capillary action when used appropriately. Consider when locating and purchasing such an adhesive to also purchase the needle-tipped dispensers often offered during the transaction.

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Ensure that your parts are solidly joined and carefully tip the applicator while the end of the applicator is in contact with the joint. You'll be able to see the glue spread throughout the length of the joined pieces.
Due to the very fast curing time, any excessive quantity that spreads to a surface will damage the surface if removal is attempted. Consider to practice on scrap or test joints to get a feel for the process.
If you intend to layer the acrylic, the same process applies, as the glue will wick into the entire surface contact points/area.
Drying time can often be measured in single-digit seconds.