We highly recommend assembling the outer frame of the rack with no glue first, just to get a feel for how all the pieces fit together and then glue them together once you’re familiar with the process.
Once you are ready to glue, a standard white wood-glue is best for gluing as it gives you more time to fit all the pieces together as compared to using crazy glue. After gluing pieces together you can use masking tape to hold things together tightly while the glue dries.