Adobe Illustrator is the best option because graphics are vectors, meaning you can size and resize your images without making them pixelated. You can create poster sized images or cake toppers with the same graphic and the quality of the graphic won't be affected.
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.