You'll need adhesives to assemble certain printables, like attaching cupcake toppers to paper straws. A printable designer's go-to adhesive is usually a hot glue gun. They're inexpensive, and the glue is guaranteed to keep everything in place. You can also use glue dots, double sided tape (permanent is preferred), glue sticks, or regular tape.
In Illustrator, you can design patterns, complex graphics and work with type. You can learn to design printables fast with the Basic Printable Design Course from Printable Crush. Illustrator is a highly in-depth program, so taking a course is a quick way to learn the basics.