For opaque acrylic, use a strong, long-lasting adhesive such as silicone adhesive caulk in white or transparent colors. Curing takes awhile, so use this on objects you can hold in place for a long period.
Transparent items require glue you cannot see. Consider one of the many all-purpose household cement gels such as Amazing Goop Adhesive.
Controlling the amount of glue is important for these items. Choose a jeweler's glue such as Beacon’s Dazzle Tac that has a small nozzle for ease of application.
The weight of items may affect your project and require quick-curing glue.
Your glue choice may require additional supplies to assemble your project. Protect surfaces under your gluing area with a cloth or mat. Have tweezers and adjustable clamps on hand to assist with positioning and holding items in place, and to prevent these strong glues from coming in contact with your skin.